Class 10th Mathematics AP Board Solution
Exercise 4.1- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- 3x + 2y = 5 2x -3y = 7 Check whether the following equation are consistent or…
- 2x - 3y = 8 4x -6y = 9 Check whether the following equation are consistent or…
- 3/2 x + 5/3 y = 7 9x -10y = 12 Check whether the following equation are…
- 5x - 3y = 11 -10x + 6y = -22 Check whether the following equation are…
- 4/3 x+2y = 8 2x + 3y = 12 Check whether the following equation are consistent…
- x + y = 5 2x + 2y = 10 Check whether the following equation are consistent or…
- x - y = 8 3x + 3y = 16 Check whether the following equation are consistent or…
- 2x + y = 6 4x - 2y = 4 Check whether the following equation are consistent or…
- 2x - 2y = 2 4x - 4y = 5 Check whether the following equation are consistent or…
- Neha went to a ‘sale’ to purchase some pants and skirts. When her friend asked…
- 10 students of Class-X took part in a mathematics quiz. If the number of girls…
- 5 pencils and 7 pens together cost D50 whereas 7 pencils and 5 pens together…
- Half the perimeter of a rectangular garden is 36 m. If the length is 4m more…
- We have a linear equation 2x + 3y-8 = 0. Write another linear equation in two…
- The area of a rectangle gets reduced by 80 sq uints if its length is reduced by…
- In X class, if three students sit on each bench, one student will be left. If…
Exercise 4.2- The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures…
- The sum of a two digit number and the number obtained reversing the digits is…
- The larger of two supplementary angles exceeds the smaller by 18o. Find the…
- The taxi charges in Hyderabad are fixed, along with the charge for the distance…
- A fraction becomes equal to 4/5 if 1 is added to both numerator and denominator.…
- Places A and B are 100 km apart on a highway. One car starts from A and another…
- Two angles are complementary. The larger angle is 3o less than twice the measure…
- An algebra textbook has a total of 1382 pages. It is broken up into two parts.…
- A chemist has two solutions of hydrochloric acid in stock. One is 50% solution…
- Suppose you have D12000 to save. You have to save some amount at 10% and the…
Exercise 4.3- 5/x-1 + 1/y-2 = 2 6/x-1 - 3/y-2 = 1 Solve each of the following pairs of…
- x+y/xy = 2 x-y/xy = 6 Solve each of the following pairs of equations by…
- 2/root x + 3/root y = 2 4/root x - 9/root y = - 1 Solve each of the following…
- 6x+3y = 6xy 2x+4y = 5xy Solve each of the following pairs of equations by…
- 5/x+y - 2/x-y = - 1 15/x+y + 7/x-y = 10 x not equal 0 , y not equal 0 Solve…
- 2/x + 3/y = 13 5/x - 4/y = - 2 x not equal 0 , y not equal 0 Solve each of the…
- 10/x+y + 2/x-y = 4 15/x+y - 5/x-y = - 2 Solve each of the following pairs of…
- 1/3x+y + 1/3x-y = 3/4 1/2 (3x+y) - 1/2 (3x-y) = -1/8 Solve each of the…
- A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can…
- Rahim travels 600 km to his home partly by train and partly by car. He takes 8…
- 2 women and 5 men can together finish an embroidery work in 4 days while 3…
- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- By comparing the ratios a_1/a_2 , b_1/b_2 , c_1/c_2 find out whether the lines…
- 3x + 2y = 5 2x -3y = 7 Check whether the following equation are consistent or…
- 2x - 3y = 8 4x -6y = 9 Check whether the following equation are consistent or…
- 3/2 x + 5/3 y = 7 9x -10y = 12 Check whether the following equation are…
- 5x - 3y = 11 -10x + 6y = -22 Check whether the following equation are…
- 4/3 x+2y = 8 2x + 3y = 12 Check whether the following equation are consistent…
- x + y = 5 2x + 2y = 10 Check whether the following equation are consistent or…
- x - y = 8 3x + 3y = 16 Check whether the following equation are consistent or…
- 2x + y = 6 4x - 2y = 4 Check whether the following equation are consistent or…
- 2x - 2y = 2 4x - 4y = 5 Check whether the following equation are consistent or…
- Neha went to a ‘sale’ to purchase some pants and skirts. When her friend asked…
- 10 students of Class-X took part in a mathematics quiz. If the number of girls…
- 5 pencils and 7 pens together cost D50 whereas 7 pencils and 5 pens together…
- Half the perimeter of a rectangular garden is 36 m. If the length is 4m more…
- We have a linear equation 2x + 3y-8 = 0. Write another linear equation in two…
- The area of a rectangle gets reduced by 80 sq uints if its length is reduced by…
- In X class, if three students sit on each bench, one student will be left. If…
- The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures…
- The sum of a two digit number and the number obtained reversing the digits is…
- The larger of two supplementary angles exceeds the smaller by 18o. Find the…
- The taxi charges in Hyderabad are fixed, along with the charge for the distance…
- A fraction becomes equal to 4/5 if 1 is added to both numerator and denominator.…
- Places A and B are 100 km apart on a highway. One car starts from A and another…
- Two angles are complementary. The larger angle is 3o less than twice the measure…
- An algebra textbook has a total of 1382 pages. It is broken up into two parts.…
- A chemist has two solutions of hydrochloric acid in stock. One is 50% solution…
- Suppose you have D12000 to save. You have to save some amount at 10% and the…
- 5/x-1 + 1/y-2 = 2 6/x-1 - 3/y-2 = 1 Solve each of the following pairs of…
- x+y/xy = 2 x-y/xy = 6 Solve each of the following pairs of equations by…
- 2/root x + 3/root y = 2 4/root x - 9/root y = - 1 Solve each of the following…
- 6x+3y = 6xy 2x+4y = 5xy Solve each of the following pairs of equations by…
- 5/x+y - 2/x-y = - 1 15/x+y + 7/x-y = 10 x not equal 0 , y not equal 0 Solve…
- 2/x + 3/y = 13 5/x - 4/y = - 2 x not equal 0 , y not equal 0 Solve each of the…
- 10/x+y + 2/x-y = 4 15/x+y - 5/x-y = - 2 Solve each of the following pairs of…
- 1/3x+y + 1/3x-y = 3/4 1/2 (3x+y) - 1/2 (3x-y) = -1/8 Solve each of the…
- A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can…
- Rahim travels 600 km to his home partly by train and partly by car. He takes 8…
- 2 women and 5 men can together finish an embroidery work in 4 days while 3…
Exercise 4.1
Question 1.By comparing the ratios
find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
5x – 4y + 8 = 0
7x + 6y – 9 = 0
Answer:We have,
5x – 4y + 8 = 0
7x + 6y – 9 = 0
Here, a1 = 5, b2 = -4, c1 = 8
a1 = 7, b2 = 6, c1 = -9
∴ ![](data:image/png;base64,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)
∴ Two line are intersecting with each at a point.
Question 2.By comparing the ratios
find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
9x + 3y + 12 = 0
18x + 6y – 24 = 0
Answer:We have,
9x + 3y + 12 = 0
18x + 6y – 24 = 0
Here, a1 = 9, b2 = 3, c1 = 12
a1 = 18, b2 = 6, c1 = -24
∴ ![](data:image/png;base64,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)
∴ Both the lines will coincide.
Question 3.By comparing the ratios
find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
6x – 3y + 10 = 0
2x - y + 9 = 0
Answer:We have,
6x – 3y + 10 = 0
2x - y + 9 = 0
Here, a1 = 6, b2 = -3, c1 = 10
a1 = 2, b2 = -1, c1 = 9
∴ ![](data:image/png;base64,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)
∴ Two line are parallel to each other.
Question 4.Check whether the following equation are consistent or inconsistent. Solve them graphically.
3x + 2y = 5
2x -3y = 7
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 3, b2 = 2, c1 = 5
a1 = 2, b2 = -3, c1 = 7
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two equations are consistent.
![](data:image/jpeg;base64,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)
Question 5.Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x - 3y = 8
4x -6y = 9
Answer:2x - 3y = 8 4x -6y = 9
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 2, b2 = -3, c1 = 8
a1 = 4, b2 = -6, c1 = 9
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ both lines are inconsistent
![](data:image/jpeg;base64,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)
Question 6.Check whether the following equation are consistent or inconsistent. Solve them graphically.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG8AAAA1CAYAAABP0LXxAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAObSURBVHja7Vs7buMwEOUBcoANILraHMCifAVbCHKAyEK6RQojILBIHcjuDCxyAXfpkiL1Fpt2G9/BN8gddk0qlPWXKImShmYxjRqRfMN5b2Y4aLPZIGMwzRyCAc+YAc+YAc+AZwwueAH1rmyM9gihf9ywvfdocAVlY0Fwd0kQOkTr54Y/XRpMtQYvoO6UEPfX/XZ7kQSSHO6C4BLCxh7m+DEJ3NHI8kXrm7fd3l/MyfxJABcHFCP0Sfz1DYhbN1ns0ns4W86DBN6SoBd20zB2frs+vT578PiBAAg7wskS4fLI11DCfafgUepNOd857jukMLRarb777uznCUg4fN0aPMZ9roU+4h6MyfIZGo8k9qG7YMnbPPVnt8KD8fzhEdomT2mDXrevAZfAPIAwdTiDPK9cxcEEL3Q+vYSLvPda7gfE/Gntkxuoa28NniB+iJwXRg38rFPIzAWPlcI4ufNaJp0K4NjmmdqEANKELHaiDivWPvPprfZ5Htvsgkx2iRQBUKUiroyZxYGEo4pTNdnIknpDK0+EbpyXC4HL5qnm0MbGyzkRjusNjN/SnD363AyqQGoSMj0vX1DxNAe7b2mlrDRes4NPfpdLkvsCL7P2r5QiUVobMM0oOodOfxIqu7AdE99sGMvJQVY49HnzIpWdEgUMWBvZf4YSPUUhU0nYjHsr6/2V/XxsYVN03+M9y7pryO3cF5jMnopCpjLOixeCHQe/Nm3g9g1etO4vVdfG8frgffWytyZXyHiuym5+GPZDbi7z+qFDZga8uocnrAo8y7L+tmkjyd68LtYuuifsv0Or3SrnUfpTuqbfQv5r1ooZ4vAizsb2noX8uutWwXlV+1fCGw52XoVia9MHHMrzZUP+ECFTSaqQ13mIvPJ4GDKSeyjwxtBB4U5f0QhQQPbJ0JANJ/VD6JCcM3QLiZ1llTAzNcWilAHAo10D1shuvAGvRXUF0hvPEsLMTglBejouO+XEFCZXxYCmoUoT1b6rG10qNehTTo3Ai2Sy6wfxzZ9eT4/7AHSYcmoMHvfaOf1RWHkA+nD1LMCrzuNghh4oU05KwItuHrADgDrl1Cl40J6L6zLl1Al4rFwEkS90mHJqBZ4Or7igTzk1Ao8lr3nqE6JBFlzS4IXJrh/oEmYgTzlJgcfLRTn9JP5ELla9gMR9kKecaoOXHtZo83Stf26DPeXUCjwGXPkbjHFXWKBPOSlJFYwZ8IwZ8Iwx+w8Fzhx5mJnkmAAAAABJRU5ErkJggg==)
9x -10y = 12
Answer:
9x -10y = 12
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 =
, b2 =
, c1 = 7
a1 = 9, b2 = -10, c1 = 12
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ both lines are consistent
![](data:image/jpeg;base64,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)
Question 7.Check whether the following equation are consistent or inconsistent. Solve them graphically.
5x - 3y = 11
-10x + 6y = -22
Answer:5x - 3y = 11 -10x + 6y = -22
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 5, b2 = -3, c1 = 11
a1 = -10, b2 = 6, c1 = -22
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two lines are consistent
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwkHBgoJCAkLCwoMDxkQDw4ODx4WFxIZJCAmJSMgIyIoLTkwKCo2KyIjMkQyNjs9QEBAJjBGS0U+Sjk/QD3/2wBDAQsLCw8NDx0QEB09KSMpPT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT09PT3/wAARCAFGAToDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2Pny+3SlO7I6daTB2dT0pSDkcnrQAfNu7dKjhzmXp98/0qTB3dT0qOEHMvJ++f6UAP52Dp2pTuyOlJg7Bye1KQcjk0AHzbj06VHDnEnT75qTB3Hk9KjhBxJyfvmgB/OwdO1B3bh0owdg5PalIO4cmgAG7celRw52P0++386kAO48mo4Qdj8n77fzoAf8ANtHTtSnduHSkwdo5PalIO4cmgAGdx6VnaLn+z5en/H1cf+jnqa11K1u7qWCGVjKmSQyFcgHBIJHIzxkVFooP2CXk/wDH1cf+jnoAvnOB07Uvzbh06UhBwOTS4O4cmgAGcnpUUOfIPTq38zUoByeTUcIPkHk9W/maAHnPHTrS/NuHTpSEHjk9aXB3Dk9KAAZyelRQZ+zDp3/nUoByeTUUAP2ccnv/ADoAkO7jp1pfm3dulBB45PWjB3dT0oABnJ6daigz9lXp0qUA5PJ61FAD9lXk9KAJTuyOnWj5t3bpQQcjk9aMHd1PSgAG7J6daihz9lTp90VKAcnk9aihB+ypyfuigCU7sjp1o+bd26UEHI5PWjB3dT0oAQZ56daZFn7NH0+6KeAeeT1pkQP2aPk/dFAEh3ZHSj5tx6dKCDkcmjB3Hk9KAGnOxunekgz5EfT7o/lSkHY3J70QA+RHyfuj+VAEfkw7PuilMEGR8oqTJ8voelKScjg9aAIvIg3fdHSmRQwkyZUffNWM/N0PSo4TzLwfvn+lADfIh2D5RSmCDI+UVJk7Bwe1KTyODQBF5EG4/KOlRwwwkPlR981Zydx4PSo4TxJwfvmgBvkQ7R8o7UpggyPlFSZ+QcHtSk/MODQBF5EG4/KKjihh2PlR95v51ZB+Y8Go4T8j8H77fzoAb5EG0fKO1KYINw+UVJk7Rwe1KSdw4NAGPZ6TJHrM17dSwvuj8oCNCpcbsqW5xlRwMepPsH6NDCbCX5R/x9XH/o561QfmPBrP0U/8S+Xg/wDH1cf+jnoAtmCDA+UUeRBuHyipCeBwe1Lk7hwelAEQggyflFRxQwmEkqOrfzNWQeTwaihP7g8Hq38zQAGCDj5R1o8iDcPlHSpCenB60ufmHB6UARCCDJ+UVHDDCbcEqM8/zqyDyeDUUB/0YcHv/OgAMEHHyjrR5EG77o6VKT04PWjPzdD0oAiEEGT8o61HDDCbZSVGcVZB5PB61FAf9FXg9KAAwQZHyjrR5EG77o6VKTyOD1pryLGGd/lVVySTwBQBha7q8GnulnaIkl/OwVF6iPPG4/4Vq29vEtnEGwzBACx7+9Yekaba6vqba70Jl3QxoRgqBgMw9T1/KuhhJ+yx8H7ooADBBkfKKPIg3fdHSniQOFZPmUnqCCKdn5uh6UARCCHn5R1qOKGH7PGSoztFWA3UY5qOFv8ARo+Dwq/0oADBBkfKKPIg3H5R0qUnkcGjJ3Hg9KAITDDtb5R3pIYITDGSoztFSk/I3B70kB/cR8H7o/lQAvzeX26U47sjp1pMfu+p6UpHI5PWgBPm3dulMhzmXp98/wBKkx83U9KjhHMvJ++f6UAP+bYOnag7sjpRj5Bye1KRyOTQAfNuPTpUcOcSdPvmpMfMeT0qOEcScn75oAf82wdO1B3bh0ox8g5PalI+YcmgBBu3HpTIc7H6ffb+dSAfMeTUcI+R+T99v50AP+baOnag7tw6UY+UcntSkfMOTQAg3bj0rP0XP9ny9P8Aj6uP/Rz1JaarbXl49vE0okUEjfGVDhTtYqSOQCQPxHrTNFH/ABL5eT/x9XH/AKOegC+d2B07Uvzbh06UhHA5Palx8w5PSgBBuyelRw58g9OrfzNSgcnk1FCP3B5PVv5mgCQ7uOnWj5tw6dKCOnJ60uPmHJ6UAIN2T0qOHP2cdO/86lA5PJqKAf6MOT3/AJ0ASHdx060fNu7dKCOnJ60uPm6npQADdk9OtRQZ+yr06VKByeT1qKAf6KvJ6UASndkdOtc14vle+sLvS4ZmiU2zyXU0cZkMceDgBRyST2HOAa3NRvI9OsnuZSxCdFHVmPAUe5NQaPYyWtu0t0c3lyfNnYevZR7AcUAcbDqMul2l1FoMljctHJB9maztljW8kYNugbHBwo3bgflBGehzs2uptc+G4xewXN5pslmWub5GCnod6+Wp3gjkYA4x7V1CoBnHGDxxUcC4tUwSPlHSgDhbPUP7GbVL+yltn0y2uoZpmskxAYWQoyqoz86fK7EHnjp0rTc+JTBaupvjI8IeUQJbbVZiTt/eEH5QQPw+tdFf6ZBqMCQXHmeSJA5RG2h8c4bHVfUd6tY+bqelAHOT2IXxvZXHmz+bcWNwrZkJEYBh+6Oi85PuaPB1stnaapBGzsqajIA0rl2b5U5LHkmuiC9eTmmQr/o0fJ+6KAHndkdKX5tx6dKCORyaMfMeT0oAad2xunekgz5EfT7o/lSkfI3J70kA/cR8n7o/lQAzyYNn+rT/AL5pTDBkfu0/75qTJ8voelKScjg9aAIvJg3f6tOn92mQwwkyZjT757VYyd3Q9KjhJzLx/Gf6UAJ5MGwfu0/75oMMGR+7T/vmpMnYOD2pSTkcGgCLyYNx/dp0/u0yGGEh8xp989qsZO48HpUcJOJOP4zQAnkwbR+7Tt/DQYYMj92n/fNSZOwcHtSkncODQBF5MG4/u0/75pkUMOx8xr95u3vVgE7jwajhJ2Px/G386AE8mDaP3adv4aDDBuH7tP8AvmpMnaOD2pSTuHBoAyNO0y4g1C6uL+a3uTNwpEbKUTOVQZJAAHp1PJp+iww/YJcxp/x9XH8P/TZ61ATuPBrP0Un+z5eP+Xq4/wDRz0AWzDBgfu0/75o8mDcP3af981IScDg9qXJ3Dg9KAIhDBk/u0/75pkUMJhOY1zlu3uasAnJ4NRQk+QeO7fzNAAYYOP3adf7tHkwbh+7Tp/dqQk8cHrS5O4cHpQBEIYMn92n/AHzUcMMJtwTGmee3vVkE5PBqKAn7MOPX+dAAYYOP3adf7tHkwbv9WnT+7UpJ44PWjJ3dD0oAiEMGT+7T/vmo4YYTbKfLXOP7tWQTk8HrWTqN7LBp8Ntaf8fl0fLh/wBn1c+wHP5UAQrFFq2t7gi/YrBto44km7/gv8zWv5MG7/Vp0/u0yys49Ps4baFTsjGMnqT3J9yeasZO7oelAEQhg5/dp1/u1HDDCbZCY1ztHarIJyeD1qKEn7KnH8IoADDBkfu0/wC+aPJg3f6tOn92pSTkcHrRk7uh6UARCGDn92nX+7TIoYfs0ZMaZ2j+GpwTzwetMiJ+yx8fwigBDDBkfu0/75o8mDcf3adP7tSknI4NGTuPB6UAQmGDY37tO/8ADSQwwmCPMaZ2j+GpSTsbg96SAnyI+P4R/KgBfm8vqOnpTjuyOR19Kbxs+929aU4yPm7+tAC/Nu6jp6VHDnMvI++f6U/jd97t61HDjMnzfxnv9KAJPm2Dkdu1Kd2RyPypvGwfN6d6U4yPm/WgBfm3HkdPSo4c4k5H3zT+Nx+bt61HDjEnzfxnvQBJzsHI7dqDu3DkflScbB83p3pTjcPm/WgBRu3HkflUcOdj9Pvt/On8bj8361HDjY/zfxt396AJPm2jkdu1B3bhyPypONo+b070pxuHzfrQAo3bjyPyrO0XP9ny9P8Aj6uP/Rz1Na6la3l5d20EjNJalVlypABOeAT16HpUOi4+wS/N/wAvVx3/AOmz0AaB3YHI7dqX5tw5HT0ppxgfN6d6XjcPm7etACjdk8j8qihz5B5HVv5mpBjJ+b9ajhx5B+bu3f3NAEh3ccjr6UvzbhyOnpSHHHzd/WjjcPm7etACjOTyPyqKDP2Ycjv/ADqQYyfm/WoocfZx83r396AJW3ccjr6Uvzbuo6elIccfN39aON33u3rQAjP5au7sqqvJJ6AYrG0SJ7wvq0wx5i+XbKR92LPX6t1/Knao39o3yaTG58s4lu2B6R9l+rH9Aa07cKtogU4AXAAPSgCY7sjkdfSj5t3UdPSkOMj5u/rRxu+929aAFG7J5HX0qKHP2VOR90VIMZPzd/WoocfZU+b+Ed6AJjuyOR19KPm3dR09KQ4yPm7+tHG773b1oABnnkdaZFn7LHyPuinDHPzd/WmRY+zR/N/CO9AEp3ZHI/Kj5tx5HT0pDjI+b9aONx+bt60AIc7G5Hekgz5EfT7o/lQcbG+b170QY8iP5v4R39qAG+VDs/1af98UpihyP3Sf98U7J8vp29acScjjv60AR+VDu/1SdP7lMhiizJmNPvn+H6VPk7unb1qOEnMvH8Z/pQAnlQ7B+7T/AL4pTFDkfuk/74p+TsHHp3pSTkcfrQBH5UO4/uk6f3KZDFFiTMaffP8ADU+TuPHb1qOEnEnH8ZoATyodo/dp2/gpTFDkfuk/74p+TsHHp3oJO4cfrQAzyodx/dJ/3xTIYotj5jT7zfw+9TgnceP1qOEnY/H8bfzoAPKh2j92nb+CgxQ7h+6T/vin5O0cenelJO4cfrQBUisY01C5uSdwmSNdhThdu7/4qq2ixRfYJf3af8fVx/D/ANNnrUBO48frWdopP9ny8f8AL1cd/wDps9AF0xQ4H7pP++KPKh3D90n/AHxTyTgcenelydw47etAEYihyf3Sf98VHDFF5JzGmct/D7mrAJyeP1qKEnyDx3b+ZoAUxQ8fuk6/3KPKh3D90nT+5TyTxx39aXJ3Djt60ARiKHJ/dJ/3xUcMUX2cExpnn+H3qwCcnj9aigJ+zDj17+9ACmKHj90nX+5VbUbi206zkuZIlIQfKoXlmPAUe5NXCTxx39ax0J1jW/Mxmz09iF9JJu5+i9PqaAJtH00Wtqz3SI13O3mTHbwGP8I9gOKtwxRG2UmNM4/u1YBOTx39aigJ+yrx29aAFMUOR+6Tr/co8qHd/qk6f3KkJORx39aMnd07etAEYihyf3Sdf7lRwxRfZkJjTO0fw1YBOTx39aihJ+ypx/CO9ACmKHI/dJ/3xR5UO7/VJ0/uVIScjjv60ZO7p29aAIxFDz+6Tr/cpkUUX2aM+Wmdo/hqYE88d/WmRE/ZY+P4R3oADFDkfuk/74o8qHcf3SdP7lSEnI4/WjJ3Hjt60ARGKHY37tO/8NJDFCYI8xpnaP4fapCTsbj170kBPkR8fwj+VAC8+X1HT0pxByOR19Kq/b7PZ/x+Qf8Af0f40pv7LI/0yD/v6P8AGgCzg7uo6elRw5zLyPvnt9Ki+32W7/j8g6f89R/jTIr+zBkzeQffP/LUe3vQBb52Dkdu1Kc5HI/Kqv2+z2D/AEyD/v6P8aU39lkf6ZB/39H+NAFnB3HkdPSo4c4k5H3z2qL7fZbj/pkHT/nqP8aZDf2YD5vIPvn/AJaj/GgC3zsHI7dqDncOR+VVvt9ltH+mQdv+Wo/xpTf2WR/pkH/f0f40AWQDuPI/Ko4c7H5H327e9Rfb7Lcf9Mg/7+j/ABpkV/ZhH/0yD7zf8tR6/WgC3g7RyO3alIO4cj8qrfb7LaP9Mg7f8tR/jQb+yyP9Mg/7+j/GgCyM7jyPyrO0XP8AZ8vI/wCPq47f9NnqwL+yyf8ATIP+/o/xqho19aLYSg3cAP2m4/5aj/nq/vQBrnOByO3alwdw5HT0qsb+ywP9Mg/7+j/Gj7fZbh/pkH/f0f40AWRnJ5H5VFDnyDyOrdvc1GL+yyf9Mg/7+j/Go4r6zEJH2yDOW/5aj1PvQBcOeOR19KXB3DkdPSqxv7Lj/TIOv/PUf40fb7Ld/wAfkHT/AJ6j/GgCyM5PI/KooM/ZhyO/b3qMX9lk/wCmQf8Af0f41B/aVtFaxlZkkLybAEkBxnJyT2AAJ/CmlcG7DdavJoIY7a0YfbLpvLi4+7/ec+wHP5VasbJNPtYraDhI1wCepPcn3J5rHtLyB9ca6uRInnIyW7yMoVFTG4YzlScg8+3Stf7fZlh/pkH/AH9H+NDi47iTT2LIByeR19Kigz9lXkdPSqEWtwve+U0bpCzsiTM4wWXOeM5A+VsE9dpph1mOERqsbywZRGnjdSoZjgADOW98dKrklewudWua5ByOR19KOd3UdPSqcWpWsgcvMkflyFDvkAB4yCDnkEEGn/b7Ld/x+QdP+eo/xqWrFJ3LIByeR19Kihz9lTkfdHaoxf2XP+mQdf8AnqP8ajhv7MWyD7ZBnaP+Wo/xpAXSDkcjr6UYO7qOnpVY39lkf6ZB/wB/R/jR9vst3/H5B0/56j/GgCwM88jr6UyLP2WPkfdHaohf2XP+mQf9/R/jTIr+z+zRj7ZBnaP+Wo/xoAuHORyPyowdx5HT0qsb+yyP9Mg/7+j/ABo+32W4/wCmQdP+eo/xoAnOdjcjv2pIM+RHyPujt7VAb+z2t/pkHf8A5aj/ABpIb+zEEf8ApkH3R/y1H+NACf2Xp+z/AI8Lb/vwv+FKdL0/I/0C2/78L/hVok7On60pJyOO/rQBU/svT93/AB4W3T/ngv8AhWbetpumTxLPpUTRzzLGJBDGACxCqADgsc84APAJrYuLeO7ieGeMPGwGVz15rKk8O29whhjkmgtg43wIwKvggg85IPHUY4oAvHS9PC/8eFt/34X/AApTpen5H+gW3/fhf8KtEkp0/Wgk5HH60AVf7L0/cf8AQLbp/wA8F/wrNvDp+nSqJtHRoWkVWmWBAq7m2qOeSc+meK17m2jvImhuIw8bYypJHespfD6G+guLed4I7ZjsgCq6Zzy3zAkMRxnsOmMmgDQOl6eF/wCPC2z/ANcF/wAKDpen5H+gW3/fhf8ACrWTsHHp3oJO4cfrQBV/svT9x/0C2/78L/hVGRNMtr62s5NMQvdO4VxbDYuAzcnHcKcDrWnc2sV7E0NxEHjOCVJIqrDpkCLb+UhjW1neRFU8ElWTnPs1AEn9l6ftH+gW3b/lgv8AhS/2Xp+4f6Bbf9+F/wAKtZO0cenelJO4cfrQBh2EulX920KaXEgKs8TtCmJVVtrEY5GCR17EU7R9NsGsZS1jbEi5uBzCv/PV/arFhosdheNMksrhVZYo3IxErtuYDAyckDr6Cl0Un+z5eP8Al6uO/wD02egCY6Xp+B/oFt/34X/Cj+y9P3D/AEC2/wC/C/4VaJOBx6d6XJ3Djt60AVBpen5P+gW3/flf8Ko6dHpl79rRNNjQ20xiYyWwXccBsgYzjDDk9a2ATuPH61VtLYRPdTrktcyb2BPAIUJx+CigAOl6fx/oFt1/54L/AIUf2Xp+7/jwtun/ADwX/CrRJ447+tLk7hx29aAKg0vT8n/QLb/vwv8AhXOJJY6pcR20Ng0KRHdOiKnMcgZBnYTgg9QeQM1e8cLcS+Er+O2cpK4VQqtgyfMMoPdhkfjXNfDbQtU0zUL25uLSSztHh8vy5AFMjg8HaPQZGfetoRXI531XTuZyk+ZRt8zprXTLu2NzLdWljM7q+0IxxjqqBduAOBk9SefTFyfRLK5jjBt1t3GGJgRVOfTOOlaTE8cd/WjJ3dO3rUObbuUopKxix6NKlwquLd7aGWSVflO+TduwjcYwN7eueOKoxQf2q09rbQ2cC20ke9kTDwSYBJQr1OOOdpHcEGuoILBl6Z4yDg1naXposvOuDPNcSzqqs8u3O1c7RwBk8nJ6mn7WV7i9mrWI7XTYJLy8lmtYzC0ipEjxDACrgkDtk5/AVb/svT93/HhbdP8Angv+FWyTkcd/Wkyd3Tt61EndlJWKo0vT+f8AQbbr/wA8V/wqhpQ0rU7eZodPh2wS+SWa3UByFU7l4+6dwwe9a0sS3EMsMyBo5AUdSeoIwRVDR9It9Kgna1VwLlxKys5YKdoXAz2wtIZYOl6fkf6Bbf8Afhf8KP7L0/d/x4W3T/ngv+FWyTkcd/Wkyd3Tt60AUpbHTIIJZZLG2CRqWY+QvAAye1UNEOmavpwuI9NtUUYAG2Nz0B525weelbUiGWGSPLLuBXcpwRkdRVLTdPFmss7TSXE9zsaSSTaCcDAGFAHAoAlOl6fkf6Bbf9+F/wAKP7L0/cf9Atun/PBf8KtEnI4/Wlydx47etAGddWml2dnPcz2VssUKM7nyF4AGT2rCTW9JVFH9l2HA7zW4P866e8to76wuLW4TdDMjRuAeoIwapR6dqBiQjWrgAgYzBF/8TQBpYPl9e3pTiDkc9/So/Mi2f6xf++6UyxZH7xf++6AHYO7r29KZCDmXn+M9vpR5sW7/AFi9P79MhkizJmRfvn+L6UATYOwc+nalIORz+lR+ZFsH7xf++6DLFkfvF/77oAkwdx57elRwg4k5/jPal82Lcf3i9P79RwyRYkzIv3z/ABUATYOwc+nagg7hz+lM8yLaP3i9v46DLFkfvF/77oAfg7jz+lMhB2Pz/G3b3o82Lcf3i/8AfdMhki2P+8X77fxe9AE2DtHPp2oIO4c/pTPMi2j94vb+OnAq5BVtw9QaAHAHcef0rO0UH+z5ef8Al6uO3/TZ6ktdUt7q8u4FEqNbMqs0ilQxIz8ueo461DoskX2CX94v/H1cfxf9NnoA0iDgc+nalwdw57elRmWLA/eL/wB90vmxbh+8X/vugB4Byef0qKEHyDz3bt7mlEsWT+8X/vumQyReSR5i5y38XuaAJiDxz39KMHcOe3pTDLFx+8Xr/frO1m/MUUdtZyr9ruj5cZ3fcH8Tn6D+lAEcQOsa2Zc5s7B9qekk2OT/AMB6fUmtSEH7OOfXt71FYwWthaR20LqI4xgfNyfUn3Jp0MkX2cAyLnn+L3oAnIPHPf0pcHd17elRmWLj94vX+/R5sW7/AFi9P79AEgByee/pUUAP2Vee3pThLFk/vF/76qKGSL7MoMi5x/eoAsEHI57+lGDu69vSmGWLI/eL1/vUnmxbv9YvT+/QA8A5PPf0qOEH7KnP8I7Uoli5/eL1/vVHDJF9mQeYudo/ioAsEHI57+lJg7uvb0ppliyP3i/99Unmxbv9YvT+/QA8A889/SmRA/Zo+f4R2oEkXP7xev8AfpkUkX2aMeYudo/ioAnIORz+lGDuPPb0qMyxZH7xf++6XzYtx/eL0/v0AKQdjc+vakgB8iPn+Efyppki2N+8Xv8AxUkMsQgjzIv3R/F7UAPwuz7n6UpC5Hyd/Sl58voOnrSnORwOvrQA3C7vudvSmQhcyfL/ABnt9Kl53dB09ajhzmXgffPf6UALhdg+T9KUhcj5P0pedg4HbvSnORwPzoAbhdx+Tt6UyELiT5f4z2qXnceB09ajhziTgffPegB2F2j5PTtQQuR8n6UvOwcDt3pTncOB+dADcLuPyfpUcIXY/wAv8bdvephnceB+dRw52PwPvt396AHYXaPk9O1VbzS7O+lVriAswGAQzLx+Bq3ztHA7d6U53DgfnQBVgso4b65uBuLThAVI4G0EDH51X0UL9gl+X/l6uO3/AE2etIZ3HgfnWdouf7Pl4H/H1cd/+mz0AXyFwPk/SjC7h8nb0pTnA4HbvS87hwOnrQA0Bcn5P0qOEL5B+Xu3b3NTDO48D86ihz5B4HVu/uaAFlaOKMu4Coo3MxHAArL0eM3txJq08ZBnXbboR9yIHj8W6/lSaqW1S+j0mP8A1QxLdkHonZP+BH9BWwAVIAAAA4AoAQBcn5P0qOEL9nHy+vb3qYZyeB+dRQ5+zDgd+/vQA8hePk7+lGF3fc7elK2eOB19aXnd0HT1oAaAuT8nf0qOAL9mX5e3pUwzk8Dr61FBn7KvA6etADyFyPk7+lGF3fc7elOOcjgdfWjnd0HT1oAaAuT8nf0qOEL9lT5f4R2qYZyeB19aihz9lTgfdHegB5C5Hyd/SjC7vudvSnHORwOvrRzu6Dp60ANAXn5O/pTIgv2aP5f4R2qQZ54HX1pkWfssfA+6O9ADiFyPk/SjC7j8nb0pxzkcD86Odx4HT1oAYQuxvk9e1JCF8iP5f4R29qcc7G4HfvRBnyI+B90fyoAXB2de3pSkHI+bvUXnQ7P9Yn/fVKZocj94n/fVAEmDu69qjhBzLz/Gf6UedDu/1idP71Rwyw5kzIn3z/F9KAJ8HYOfSlIORzUXnQ7B+8T/AL6pTNDkfvE/76oAkwdx+bt6VHCDiTn+M0edDuP7xOn96o4ZYcSZkT75/ioAnwdg59KCDuHNR+dDsH7xO38VKZocj94n/fVAD8HceaZCDsfn+Nv50edDuP7xP++qjilh2PmRPvN/F70AT4O0c+nagg7h81R+dDtH7xO38VPUo5BQhh6g5oAcAdx5rO0UH7BLz/y9XH/o56baaus+oy2s1tLbME81DIw+ZN23JAPy5I4B6j6HCaLLCLCXMif8fVx/F/02egDTIOBz6UuDuHzdvSojNDgfvE/76pfOh3D94n/fVAEgByeao3d6unaXJcSZbaSFQdXYkgKPqaZq+s2mi6Xc38x8xIVB2RkFmJOAB9SQK5Tw74oj8T66kV5ALUWsbTwR+ZvWRs4JJwOVBGB7k1ahJxcktES5xTUW9WdZpNhJZ2m+4bdd3D+bOw7sew9gOB9Kv4O4c9qjM0PH7xOv96l86HcP3idP71QUSAHJ5qKAH7OOfX+dKJocn96n/fVRwyw/ZxmRM8/xe9AE5B4570uDu69qjM0PH7xOv96jzod3+sTp/eoAkAOTz3qKAH7KvPalE0OT+8Tr/eqKGWEWygyJnH96gCyQcjnvRg7uvaozNDkfvE6/3qPOh3f6xOn96gCQA5PPeooQfsqc/wAIpRNDk/vE6/3qjhlhFsmZEztH8VAFgg5HPejB3de1RmaHI/eJ/wB9UedDu/1idP71ADwDzz3pkQP2aPn+EUgmh5/eJ1/vUyKWH7NGPMTO0fxUAWCDkc0YO4/N2qMzQ5H7xP8Avqjzodx/eJ0/vUAOIOxufWkgB8iPn+Efyphmh2N+8Tv/ABUQzQiCPMiZ2j+L2oAkz+76HpSk8jg9aT5vL7dKcd2R060AJn5uh6UyE8y8H75/pT/m3dulMhzmXp98/wBKAHZ+QcHtSk8jg0fNsHTtSndkdKAEz8x4PSmQniTg/fNSfNuPTpUcOcSdPvmgB+fkHB7UE/MODR82wdO1B3bh0oAAfmPBqOE/I/B++386k+bcelMhzsfp99v50APz8o4Paqt5pllfyq93aJKyjALDOBVr5to6dqDu3DpQBnaXpP8AZk9zILqeczsXfzVTOe3IAJwOAOwpdFP/ABL5eD/x9XH/AKOetEbtx6VnaLn+z5en/H1cf+jnoA0CeBwe1GfmHB6UHdgdO1NllECNLKyrGilmYngAdaAMjxMqX2nnSfLEkuofu1U/wqOS/wDwHqPfFVvDXhDT/DzS3Nu1xPcSKY/MmIJVc9AAABnAz9Ku6NFJdzS6tcLtkuAFgRuscPb8T1P4Vow58g9OrfzNUpSScU9BOKbvbUkJ6cHrRn5hwelB3cdOtHzbh06VIwB5PBqOA/6MOD3/AJ1KN2T0qKDP2YdO/wDOgCQnpwetGfm6HpQd3HTrS/Nu7dKAEB5PB61HAf8ARV4PSpRuyenWooM/ZV6dKAJCeRwetGfm6HpSndkdOtHzbu3SgBAeTwetRwn/AEVOD90VIN2T061HDn7KnT7ooAkJ5HB60Z+boelKd2R060nzbu3SgAB68HrTIj/o0fB+6KeM89OtMiz9mj6fdFADyeRwaM/MeD0pTuyOlHzbj06UANJ+RuD3pID+4j4P3R/KlOdjdO9JBnyI+n3R/KgB2D5fU9KUg5HJ61D50Gz760pngyPnX86AJcHd1PSo4Qcy8n75/pSefBu++vT1pkM0IMmXX75oAnwdg5PalIORyah86DYPnX86UzwZHzr+dAEuDuPJ6VHCDiTk/fNJ58G4/OvT1pkM0ID5dfvmgCfB2Dk9qUg7hyah86DaPnXt3pTNBkfOv50ASgHceTUcIOx+T99v50nnQbj86/nUcU0IR8uv3m/nQBYwdo5PalIO4cmovOg2j517d6cJImIIYEUAPAO48ms/RQf7Pl5P/H1cf+jnqOz1lLjU7qzmg8iSFVfmQN8pJAzjoTjOOeD+FJos0IsJfnX/AI+rj/0c9AGoQcDk9qx9SzqupJpaEmCMCW7PqP4U/HqfYVa1LU4LCxaYYkk4WOMHl3PQUzSbeKwtQJpVe5lJknk/vOev4DoPYUAaIXBIBwKjhB8g8nq38zQJoMn51/Oo4poRCQXXOW/maALBB45PWlwdw5PSojNBx869fWjzoNw+denrQBKAcnk1FAD9mHJ7/wA6BPBk/Ov51HDNCLcAuuef50AWSDxyetGDu6npURmg4+devrR50G7769PWgCUA5PJ61FAD9lXk9KBPBk/Ov51HDNCLZQXXOKALJByOT1owd3U9KiM8GR869fWjzoN3316etAEoByeT1qKEH7KnJ+6KBNBz869fWo4ZoRbIC652igCyQcjk9aMHd1PSojPBkfOv50efBu++vT1oAkAPPJ60yIH7LHyfuikE0HPzr19aZFND9mjBdc7RQBYIORyaMHceT0qIzQZHzr+dHnwbj869PWgB5B2Nye9EAPkR8n7o/lUZmg2N869+9JDNCIY8uudo70ATZOzoelKScjg9ab83l9ulOO7I6daADJ3dD0qOE8y8H75/pT/m3dulMhzmXp98/wBKAH5OwcHtSknI4NJ82wdO1Kd2R0oAMnceD0qOEnEnB++ak+bcenSo4c4k6ffNAD8nYOD2pSTuHBpPm2Dp2oO7cOlACgnceDUcJOx+D99v50/5tx6UyHOx+n32/nQA/J2jg9qr3WnWV7Kr3dlBOwGAZI1YgfjVj5to6dqDu3DpQBRs9Jhs717gPcSybDGnmybhGpbcVX2zjrnoKTRSfsEvB/4+rj/0c9aA3bj0rmxcTNp/9nWjbbm7urkbh/yzjEz7n/oPc0AW7Y/2vqxvSC1paMY7cdnk6M/4dB+NbOTuHBqvFHDYWsNvGY4okARATjpWFeeJb6wuta+02USRWNos9uoky0uWdQWI4UEoOOSAefQAHSgnJ4NRwk+QeD1b+ZrAHiObSZ7uHXTCy24hd7m3jKoiSbhlwWJADIQTk8EHjmiXxjp1jDYC7c2zXrEhJ/keNCHIZh2B24x15FAHREnjg9aXJ3Dg9K5VPFU8+tvDE1uLaO7Np5bwybpGC5OJfuBieiHqO4yK0Y/E9vcRxSWtvdXHmWy3OyKMFlVmwARnrkNx/smgDZBOTwaigJ+zDg9/51BY6kt3GXkhmtSX2hLlQjN06DJz1rDg1XW0vGsfKsJ7qS1knECFgLY7gEDvk7g2TyAD8pxx0AOoJPHB60ZO7oelY+iald3tzf29y9vOLSZYxcwIUR225ZcEnlTwcHv6g1sfNu7dKAAE5PB61FAT9lXg9KlG7J6daigz9lXp0oAlJORwetGTu6HpQd2R060fNu7dKAAE5PB61FCT9lTg/dFSDdk9OtRw5+yp0+6KAJSTkcHrRk7uh6UHdkdOtJ827t0oAATzwetMiJ+zR8H7op4zz060yLP2aPp90UASEnI4NGTuPB6UHdkdKPm3Hp0oAaSdjcHvRAf3EfB+6P5UHOxunekgz5EfT7o/lQAuP3fU9KcRyOT1qHzodnX/AMdNKZ4cjn/x00AS4+bqelRwjmXk/fP9KTz4d3Xt/dNMimhBkyf4z/CaAJ8fIOT2pSORyah86HYOf/HTSmeHI5/8dNAEuPmPJ6VHCOJOT980nnw7jz2/ummQzQgPk/xn+E0AT4+QcntQR8w5NRefDtHPp/CaUzw5HP8A46aAJQPmPJqOEfI/J++386Tz4dx5/wDHTUcU0IR8n+Jv4T60AWMfKOT2pSPmHJqHz4do59P4TQbi3DDdIi/7xx/OgBZ5o7WGWeaTbHGu5mPYCsTwrbCS0udScOJbuaUhW6xJ5jfL+eT+NRNqMXiHWpbGNR/Z9k6vNKDkTvzhQP7oI5PfFaGjTRfYJcn/AJerj+E/89noAuXmm2d/5JvLWC4MTBozLGr7D6jI4NVrzQra+ubx7hpGW8tRayJnACgscg9QfnP5CrpnhwOf/HTR58O4c/8AjpoAxm8Jw3Kyrf3tzeee6G483aPORAdsZCgDbk5OOpzng4q5Y6VFDp9nDJLNcGydmhklb5hjcoyR1wrEc9frV0Tw5PP/AI6ajimhEJBPdv4T6mgDPfw1AdQ88XNwLdrkXbWoK7GmGMNnG7qAcZxkZqvonhuJLS9/tO0iY31w07W0mJViXOVTpjgkt7FjW4Z4eOe/900efDuHPb+6aAKaeHtIjCKmmWSiGTzIwIE+R+PmHHB4HPsKyrHwpPbabeQJrl6Bdh/MlEcSyl2PL7wuS2OB6Dp0FdCJ4cnn/wAdNRwzRC3AJ55/hPrQBX0bSX0ezW1+1tNCmBEvlJGIx6AKB+taOPm6npURnh457/3TR58O7r2/umgCUDk8nrUUA/0VeT0oE8OTz/46ajhmiFsoJ5x/dNAFkjkcnrSY+bqelRmeHI57/wB00efDu69v7poAlA5PJ61FCP8ARU5P3RQJ4eee/wDdNRwzQi2QE87R/CaALJHI5PWjHzdT0qIzw5HP/jpo8+Hd17f3TQBIB15PWmRD/RY+T90Ugnh557/3TUcU0P2eMZ52j+E0AWSORyaMfMeT0qIzw5HP/jpo8+Hcee3900API+RuT3pIB+4j5P3R/KmGaHa3Pr/CaSGeEQxgn+EfwmgCbJ2dD0pSTkcHrTfm8vqOnpTjuyOR19KADJ3dD0qOEnMvB++f6VJ827qOnpUcOcy8j75/pQA/J2Dg9qUk5HBpPm2Dkdu1Kd2RyPyoAMnceD0qOEnEnB++ak+bceR09KjhziTkffNAD8nYOD2pSTuHBpOdg5HbtQd24cj8qAFBO48Go4Sdj8H77fzqQbtx5H5VHDnY/I++386AH5O0cHtWXrxtYrcSy2UFzcufKgWSNWLOeg57dzWpztHI7dqx7DOrao2pNzbQ7orQEcN2aT8eg9qAH6H4etNE3SQwoLqSNVmkUAbsEngdhlj+Q9Km0Un7BLwf+Pq4/wDRz1oDO48j8qztFz/Z8vI/4+rj/wBHPQBoEnA4NLk7hwelId2ByO3al+bcOR09KAAE5PBqKEnyDwerfzNSjduPI/Kooc+QeR1b+ZoAkJPHB60uTuHB6UhzxyOvpS/NuHI6elAACcng1FAT9nHB7/zqUZyeR+VRQZ+zDkd/50ASknjg9aMnd0PSkbdxyOvpS/Nu6jp6UAAJyeD1qKAn7KvB6VKM5PI6+lRQZ+yryOlAEpJyOD1oyd3Q9KDuyOR19KPm3dR09KAAE5PB61FCT9lj4P3RUo3ZPI6+lRQ5+ypyPuigCUk5HB60ZO7oelB3ZHI6+lHzbuo6elACAnng9aZET9mj4P3RTxnnkdfSmRZ+yx8j7ooAkJORwaMnceD0oO7I5H5UfNuPI6elADSTsbg96SAnyI+P4R/KlOdjcjv2pIM+RH0+6P5UALj931PT1pSORyevrUfnRbOh/wC+D/hQZosjhv8Avg/4UASY+bqenrTIRzLyfvn+lJ50W7o3T+4f8KZDNHmThvvn+A/4UATY+Qcnt3pSORyfzqPzotg4b/vg/wCFBmiyOG/74P8AhQBJj5jyenrTIRxJyfvnvSedFuPDdP7h/wAKZDLHh+D98/wH/CgCfHyDk9u9BHzDk/nUfnRbRw3b+A/4UGaLI4b/AL4P+FAEgHzHk/nUcI+R+T99u/vR50W48N/3wf8ACq8l/bWdnPcTkiOMsxOw+tAFbWJXuGh0q2dlluRmVweY4h94/U9B9a0ooI7eOOGIbI0XaqjoAKzNHiKRyXt4rC7uyGddh/dr/Cg47D9c1flvrOFlE08MRI4EjBSfwNAE4HzHk/nWfoo/4l8vJ/4+rjv/ANNnqDTNYa8vbiK4hWDaWMSFJA7IHK7uVAIPB4JxkVJo0sYsJeD/AMfVx/Af+ez+1AGmRwOT270Y+Ycnp61GZosDhv8Avg/4UedFuHDf98H/AAoAkA5PJ/Oo4R+4PJ6t39zQJosnhv8Avg/4UyKWPyTwerfwH1PtQBOR05PX1ox8w5PT1qMzRccN1/uH/Cjzotw4bp/cP+FAEgHJ5P51HCP9HHJ79/egTRZPDf8AfB/wqOGWMW4GD3/gPr9KALBHTk9fWjHzdT09ajM0XHDdf7h/wo86Ld0bp/cP+FAEgHJ5PX1qOAf6KvJ6etKJosnhuv8AcP8AhUUMsYtlGDnH9w/4UAWCORyevrRj5up6etRmaLI4br/cP+FHnRbujdP7h/woAkA5PJ6+tRwj/RU5P3R3oE0XPDdf7h/wpkMsYtkGDnaP4D/hQBORyOT19aMfN1PT1qMzRZHDf98H/Cjzot3Run9w/wCFAEgHXk9fWo4h/o0fJ+6O9Ami54br/cP+FMilj+zxjBztH8B/woAnI5HJ/OjHzHk9PWozNFkcN/3wf8KPOi3Hhun9w/4UAPI+RuT370kA/cR8n7o/lTDNHtbhu/8AAf8ACkhmjEEfDfdH8B/woAlydnTt604k5HHf1puD5fUdPSnEHI5HX0oATJ3dO3rTIScy8fxnv9Kkwd3UdPSo4c5l5H3z2+lAD8nYOPTvQScjj9aMHYOR27UpByOR+VABk7jx29ajhJxJx/Ge9SYO48jp6VHDnEnI++e1AD8nYOPTvQSdw4/WjB2Dkdu1BB3DkflQAZO48frWIwOr6sbfGbOxkLy+kkucqv0HU++Ku6vfSWVuFtwHup2EUCEdWPc+wHJ+lO0myFhp4gRtxVmLuRy7E8sfqaALmTtHHp3qOa2hndTNbxSEDGXUGpMHaOR27UpB3DkflQBSs9KtrK5eaFJPMYFQXlZgik5IUE8DPOB7egqPRSfsEvH/AC9XHf8A6bPWiAdx5H5VnaLn+z5eR/x9XHb/AKbPQBoEnA49O9Lk7hx29aQg4HI7dqXB3DkdPSgBATk8frUcJPkHju3f3NSgHceR+VRQ58g8jq3b3NAEhJ447+tGTuHHb1oIPHI6+lLg7hyOnpQAAnJ4/WooSfs449e/vUoByeR+VRQZ+zDkd+3vQBISeOO/rRk7unb1oYHjkdfSlwd3UdPSgABOTx39aigJ+yrx29alAOTyOvpUUGfsq8jp6UASknI47+tJk7unb1pSDkcjr6UYO7qOnpQAAnJ47+tRQk/ZU4/hHepQDk8jr6VFDn7KnI+6O1AEpJyOO/rSZO7p29aUg5HI6+lGDu6jp6UAICeeO/rTIifs0fH8I708Z55HX0pkWfssfI+6O1ADyTkcfrS5O48dvWgg5HI/KjB3HkdPSgBpJ2Nx696SAnyI+P4R/KlOdjcjv2pIM+RHyPujt7UALgeX17etKQMjnv61H5qbPuP/AN+z/hSmZMj5H/79n/CgB+Bu69vWmQ4zLz/Ge/0o85N33H6f88z/AIUyGVcyfI/3z/AaAJcDYOfTvSkDI5/Wo/NTYPkf/v2f8KUzJkfI/wD37P8AhQA/A3Hnt61HCBiTn+M96Xzk3H5H6f8APM/4VHDKoD/I/wB8/wABoAmwNg59O9DFVwS2AMkkmmeam0fI/b/lmf8ACsTUdSh1e5GkWbsSWIu2VSCkY6jp1J4/OgCxpa/2nfyatJnygDFaKT0Tu/8AwI/oK04QNj8/xt396SNoo1CJG6oqgKBGcAflTYZV2P8AI/3m/gPrQBPgbRz6d6CBuHP61H5qbR8j9v8Almf8Kin1KytpFW5uYYGIyFlcISPoaALIA3Hn9az9Fx/Z8vP/AC9XHf8A6bPVTRPEB1W4k3QrHEyl4QEfcyhipPTBHTkdM9+tWNFlX7BL8j/8fVx/Af8Ans9AGmQMDn070YG4c9vWmGVMD5H/AO/Z/wAKPOTcPkf/AL9n/CgB4Ayef1qOEDyDz3bv7mlEqZPyP/37P+FRxSr5J+R+rfwH1NAE5A457+tGBuHPb1phlTj5H6/88z/hR5ybh8j9P+eZ/wAKAHgDJ5/Wo4cfZhz69/elEyZPyP8A9+z/AIVHDKotwNj9/wCA+tAE5A457+tGBu69vWmGVOPkfr/zzP8AhR5ybvuP0/55n/CgB4Ayee/rUcAH2Vee3rSiZMn5H/79n/Co4ZVFso2P0/uGgCcgZHPf1owN3Xt60wzJkfI/X/nmf8KPNTd9x+n/ADzP+FADwBk89/Wo4cfZU5/hHelEyZPyP1/55n/Co4ZVFsg2P90fwGgCcgZHPf1owN3Xt60wzJkfI/8A37P+FHnJu+4/T/nmf8KAHgDnnv61HEB9mj5/hHelEqc/I/X/AJ5n/Co4pV+zRjY/3R/AaAJyBkc/rRgbjz29aYZkyPkf/v2f8KPOTcfkfp/zzP8AhQA4gbG59e9JAB5EfP8ACO/tTTKmxvkfv/yzNJDKogj+R/uj+A+lAEmT5fT9acScjjv603B8vr29KcQcjnv6UAGTu6dvWo4Scy8fxnv9Kfg7uvb0pkIOZef4z2+lAD8nYOPTvSknI4/Wkwdg59O1BByOf0oAXJ3Hjt61HCTiTj+M96kwdx57elRwg4k5/jPagBt1Obaykm2Fiibgo5JPYVieHPDp09vt18A99LljzxHnr+Pqa6DB2Dn07UEHcOf0oAUE7jx+tRwk7H4/jbv708A7jz+lMhB2Pz/G3b3oAfk7Rx6d6RkDsN0an60uDtHPp2oIO4c/pQBUtNLtLK5kmt4AkjggneSACckKDwoJOcDHNRaKT/Z8vH/L1cd/+mz1oAHcef0rP0UH+z5ef+Xq47f9NnoA0CTgcenelydw47etIQcDn07UuDuHPb0oAQE7jx+tRwk+QeO7d/c1IAcnn9KjhB8g8927e5oAkJPHHf1pcncOO3rSEHjnv6UYO4c9vSgBQTk8frUUBP2Ycevf3qQA5PP6VHAD9nHPr296AJGJ447+tLk7unb1pCDxz39KMHd17elACgnJ47+tRQE/ZV47etSgHJ57+lRQA/ZV57elAEpJyOO/rSZO7p29aUg5HPf0pMHd17elACgnJ47+tRQk/ZU4/hHepADk89/So4Qfsqc/wjtQBKScjjv60ZO7p29aCDkc9/Skwd3Xt6UAAJ547+tMiJ+yx8fwjvTwDzz39KZED9mj5/hHagCQk5HH60ZO48dvWkIORz+lLg7jz29KAGknY3Hr3pIM+RHx/CO/tSkHY3Pr2pIAfIj5/hH8qAHbR5ffp60pUZHXr60UUAG0bu/T1qOEDMvX757/AEoooAftGwde3elKjI6/nRRQAbRuPXp61HCBiTr9896KKAH7RsHXt3pSo3Dr+dFFAAFG49fzqOEDY/X77d/eiigB+0bR17d6UqNw6/nRRQABRuPX86ztFA/s+Xr/AMfVx3/6bPRRQBoFRgde3el2jcOvT1oooAAo3Hr+dRQgeQevVu/uaKKAJCo469fWl2jcOvT1oooAAoyev51FAB9mHXv396KKAJGUcdevrS7Ru79PWiigACjJ69fWooAPsq9enrRRQBKVGR16+tG0bu/T1oooAAoyevX1qKFR9lTr90d6KKAJSoyOvX1o2jd36etFFACBRz16+tMiUfZY+v3R3oooAkKjI6/nRtG49enrRRQA0qNjde/ekgA8iPr90d/aiigD/9k=)
Question 8.Check whether the following equation are consistent or inconsistent. Solve them graphically.
![](data:image/png;base64,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)
2x + 3y = 12
Answer:
2x + 3y = 12
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 =
, b2 = 2, c1 = 8
a1 = 2, b2 = 3, c1 = 12
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two equations are consistent
![](data:image/jpeg;base64,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)
Question 9.Check whether the following equation are consistent or inconsistent. Solve them graphically.
x + y = 5
2x + 2y = 10
Answer:x + y = 5 2x + 2y = 10
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALsAAAA2CAIAAAAQ3H87AAAAAXNSR0IArs4c6QAABLlJREFUeF7tXTtOJDEQ3dlzIIQYToGAEDgCZKQQI0gISeAAcAQIOABMCiLgDICIuAa8VUnG6xna5XZ12d1dHaxGM+X6PD+Xq5ty7+Tr6+uPXYYAG4G/bEkTNAT+IWCMMR6kITBxu9JkMkkbatJjQuCHJz5jStU0IKumaWVzfF71wjHblfgTapJWxxgH0hGwHJOO2bhHGGPGPf/p0feAMU9PTygJ6drd3U2PseWIy8tLTXPNXr6/vzsQ6AO+aRlY3rDaGQNcNjc3b25ucDOF6/X1VW0WT09P87CVHH13d3dxcUEg4Do8PJxOp5IG+LqcExjiPit/aDANaHZ2dpw/j4+PEH57e8vxMBqpQ883nWOROTbqmNODJZSPA9MrevDhhOM55vb2Fjnw6OjI4Yh0jW/wPZ+XrSVns9nq6qobvrGxgc8vLy+tFXIGEjqgC0e4iMzZ2RnWko+MnhucHEOMpq2BPmOt8xkalWxYW/jJz8bE9+CbqP5AgLmUwZjacgylWHH8owCm5RhI7+3tYZL29/dRhOJfkIbWeqnr4+OjlOmydgE7ze75+fna2loRZ+K7Erl1cnKCBYciFMkQBCriqzO6srJS1oHi1q+urlDM6RQGQbBcxpTCCHcE8xlleXm5lD9ml8sYVL4PDw/YR6+vr1H5qgG3vb3tP3jAtgjTS0tLag7Uaejz87MYDvzKl+5pUdCIV15+YRVUYTCKX93zGKSc/Gq0wZxvvarKF874dxsIIR+HaMG7kBs/99m/4UgUcXPmbjv9b/i2F0o2T6G7QZCCKcqY+bySGSBzeINjdIvqLlSTTJ0iYr5j/3VU0b2r/qXcF6Jsjo9nLxzj1jH8sE1y2AgYY4Y9v/LRGWPkMR22RmPMsOdXPjpjjDymw9ZojBn2/MpHZ+eV5DEdpEb35MWex1Q0v/Y8pqLJMFekELA6RgrJsegxxoxlpqXiNMZIITkWPbUzZv6cDspDtQYddAXBHDXllL38Q1vK57aCwGtnDLkbdFaghVRh/sBLtI8pGOKYeH5+9vvhNc9the5xOqpEeiwalMCn334NOqpEPGkw5/RTU04X7WPtcAhGVX1eiU4nBa2TaueVOOtPXMYdxFxfXxdX3nuFnByDXsngCKdsy2A0x/go56eZaI6h7AJDlGlkD2eJ5Bjgj0nJh4KpwUcs3rXpentJe6ltgqzTYWNmnL+JNWvw23vrZMx8H20mINHhyYzxWQJ3xdnNJ4EIXxvMBdFVyBiqYDJPhUYpEggkMwbj3Yn5YIdKtb1Qns8YDM/Hq5kxC+sM8UXSDocidCHMf6oXTh3jdnTKhyIs8ZXwdXadY4LQqsox+pvRQm6w6hgaSe866OLcQwNjYM5/GIO1nr/c+QSthzHAQbMGb9iVEp7gHRwcwOnj42PN+8OtrS28G8C9nglHJPHwStOBSmzhrSjwBOfe/TdV+a9oUfMzoT+GXg51f38v7pxyX4iyOT5cvXCMyxg81MJ2gCzdxXtAlJFSNjdSxiDBYDvoaEdQnkJlcyNlDD/sFpLKU6hsjg9ILxxLqHz5kZvkgBEwxgx4cjsJzRjTCawDVmrnlQY8uZKh0d8KcKn+x0aSEZiuQgjYrlQI+N6a/QbKsm+yUq5uagAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK4AAAA2CAIAAADRWzWXAAAAAXNSR0IArs4c6QAABLBJREFUeF7tXEEyLEEQNf8cQgicQmCJI7CzZS3YWNpwAI7AwgGwJSycAWHlGrwfKVKqGVXZXVXZ0z3ZC9ExqvJlvnqdlV1TNaPPz885v5yBubl/ToIzQAy4FFwJ3wyMeIIYjUbOygwy8CMAKYWu6gao0BLaGA7yskdUalo65hOEkrThN3MpDH+MlRG6FJREDb+ZS2H4Y6yMsAdSeHx8RHVD1/b2tjKw/Gbn5+cGcG9vbxwd3eCTfOdbWJh2KYCX9fX1q6srvGLgenl5MRge4vH4+LgFoU273NzcnJ2dUXS49vf3l5eXmxop056dgDm+N76JQIOara0t9ufh4QGNX19fczxMRsrMSuiqiGwcos8PUO+qpCKdFa6vr5G1Dg4OmCBkTnyCz8uIMWrl/v5+aWmJm6ytreH++fm5KjRRCR1URZlo/OTkBOqXIdv5oMkKJFXK0nSPp1MvvWTLyGOKf8n8SStRwSdJ+0GDZFZgKZhlBcp2xYlNMtMsK6D1zs4O2N/d3UUFh79QAz2dXV3v7+9dQVfCBZ80bKenpysrK5VQ4mbTEwT1Pzo6wiOCCg7pC8roxFcGXVxc7NaBeugXFxeohGwm3yAKrRTqBR+3jHJ6PAcsLCx05c+AcbVSQNl4d3eHKe3y8hJloxkjm5ub8j0bMxSg5+fnzRwwBvr4+OgsQH3ZSK9wKBqKVzeyeAkqHYDiv7yugCSRX8pF4CQ6gPKxyGAEERCyBkfLUqDJmjFw7Gct4S93aex5MPgtS36iQY20iY8NV9elaEpKYTwT1AuQ3sj4QimWidWou6Ti19YVkon9Zfx1vjEc+LRHVA6i71dQEjVbzbRl42yxMpPRuhRmctgnBe1ScCl8M+BScCm4FFwDvxnwcxCzrgheQfB1BQsp+LqCBcuOUYoBLxtLMdl7Oy6F3g9hqQBcCqWY7L2daZfC+DEBlGBmGyawSwNwtEmi0iVPeRgf9AgimnYpkLvBF+LYXVdpYKRZCA77dGoDPT09yV27lgc9wtA0W1cafQXeojF8+qtXsHWlhfHxLhE4bkybJErt09EgEvRUn4OgUw/BrjKzcxC1H8qJ9vlI1urqaicOdAOqyQrYRhYc5iq76SqZFSQ1+Ykh+YxSPgAQ5Yb8Qx9JRA4KxILt/BiVFqRj6Q1tMEp5kqx3lbEJnc4TKuP8q1ncgtzSaCyF8b2DmZEmuzeWghx+uFtctvrRLSLECFwQnaUUqErIPPiVHPugQWMpoD8fYw0mi6bYE9vrpYDu+XzFpTBxns5UfzLATnRAZP5UCJpagWdNOVMUEQEZSTLFWLWzQhCUTVawnxcmDrqqVqCedLK4xu7siBQAJxcV8HRmPqCNlGcgBQRYpDJt92RK5hssMe3t7aHn4eGh5avOxsYGDuzy75LgsBQWYSwdqI2FXw0ABA6jyt9ekT9hUNsBtt9gvwL93Mnt7W1x54y/zjeGA132iMoxko5ppYBVF2RmJMwax+mNmTKGG5oUkBKQmSslZ+OxMYYbmhSUCaddM+OxMYbrixQalI3thtl79YUBl0JfRqq6n775vTrFUw5ACy3/ZzG+m3KP3b3aDPgEUZvh3th3KfRmqGo7+gWtxMRB/hXkGAAAAABJRU5ErkJggg==)
Here, a1 = 1, b2 = 1, c1 = 5
a1 = 2, b2 = 2, c1 = 10
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two lines are inconsistent
![](data:image/jpeg;base64,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)
Question 10.Check whether the following equation are consistent or inconsistent. Solve them graphically.
x - y = 8
3x + 3y = 16
Answer:x - y = 8 3x + 3y = 16
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 1, b2 = -1, c1 = 8
a1 = 3, b2 = 3, c1 = 12
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two lines are inconsistent
![](data:image/jpeg;base64,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)
Question 11.Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x + y =
6 4x - 2y = 4
Answer:2x + y = 6 4x - 2y = 4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 2, b2 = 1, c1 = 6
a1 = 4, b2 = -2, c1 = 4
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two lines are consistent
![](data:image/jpeg;base64,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)
Question 12.Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x - 2y =
2 4x - 4y = 5
Answer:2x - 2y = 2 4x - 4y = 5
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Here, a1 = 2, b2 = 2, c1 = 2
a1 = 4, b2 = 4, c1 = 5
∴ ![](data:image/png;base64,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)
![](data:image/png;base64,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)
∴ two lines are inconsistent.
![](data:image/jpeg;base64,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)
Question 13.Neha went to a ‘sale’ to purchase some pants and skirts. When her friend asked her how many of each she had bought, she answered “The number of skirts are two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased.”
Help her friend to find how many pants and skirts Neha bought.
Answer:Let the number of pants purchased by Neha be ‘x’ and no. of skirts purchased be ‘y’.
Twice the number of pants = 2x
From the given condition,
y = 2x – 2 (I)
i.e. number of skirts are 2 less than 2 twice the number of pants.
y = 4x – 4 (II)
i.e. number of skirts are 4 less than four times the number of pants.
Subtracting eq. I from II, we get
2x = 2
⇒ x = 1
So number of pants purchased = 1 and number of skirts = 0
Graphical Representation:
Question 14.10 students of Class-X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys then, find the number of boys and the number of girls who took part in the quiz.
Answer:Let the number of girls and boys in the class be x and y respectively
According to given condition, we have:
x + y = 10
x-y = 4
x + y = 10 ⇒ x = 10-y x-y = 4 ⇒ x = 4 + y
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)
From the graph it can be observed that the two lines intersect each other at the point (7, 3)
So, x = 7 and y = 3
Number of Girls = 7;
Number of boys = 3
Question 15.5 pencils and 7 pens together cost D50 whereas 7 pencils and 5 pens together cost D46. Find the cost of one pencil and that of one pen.
Answer:Let the cost of one pencil and one pen be ₹x and ₹y respectively.
According to given situation, we have :
5x + 7y = 50
7x + 5y = 46
5x + 7y = 50 7x + 5y = 46
![](data:image/png;base64,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)
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)
From the graph. It can be observed that the two lines are intersecting each other at (3,5)
x = 3 and y = 5
Cost of pencil = ` 3;
Cost of pen = ` 5
Question 16.Half the perimeter of a rectangular garden is 36 m. If the length is 4m more than its width, is 36 m. Find the dimensions of the garden.
Answer:Let l be the length and b be the breadth
l = b + 4
l-b = 4
Perimeter = 2(l + b)
× 2(l + b) = 36 (given)
l-b = 4 ……I
l + b = 36 ….II
adding eq. I and II
⇒ 2l = 40
⇒ l =
= 20m
Substitute l = 20 in(1)
l-b = 4
20-b = 4
b = 20-4 = 16m
Length = 20 m
Width = 16 m
Question 17.We have a linear equation 2x + 3y-8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.
Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.
Answer:2x + 3y-8 = 0
3x + 2y-7 = 0(intersecting)
2x + 3y + 12 = 0 (parallel lines)
4x + 6y-16 = 0 (coincident lines)
Question 18.The area of a rectangle gets reduced by 80 sq uints if its length is reduced by 5 units and breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area will increase by 50 sq units. Find the length and breadth of the rectangle.
Answer:Let the length be x and breadth be y
According to question,
xy-80 = (x-5)(x + 2)
⇒xy-80 = xy + 2x-5y-10
⇒-80 + 10 = 2x-5y
⇒ 2x-5y = -70 ….I
(x + 10)(y-5) = xy + 50
⇒ xy-5x + 10y-50 = xy + 50
⇒ -5x + 10y = 100
⇒ -x + 2y = 20 ….II
Multiplying Eq. II by 2
2x-5y = -70
-2x + 4y = 40
-y = -30
y = 30
substituting y = 30 in eq. II
-x + 2× 30 = 20
-x = 20-60
x = 40
length = 40units and breadth = 30 units
Question 19.In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.
Answer:Let the number no. of students be x
Let the number no. of benches be y
According to given condition, we have
x = 3y + 1 ⇒ x-3y = 1 …..I
x = 4(y-1) ⇒ x = 4y-4 ⇒ x-4y = -4 ….II
Equating eq. I and II
x-3y = 1
-x + 4y = 4
y = 5
Substituting y = 5 in eq. I
x-3×5 = 1
⇒ x-15 + 1 ⇒x = 16
Number of students = 16;
Number of benches = 5
By comparing the ratios find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
5x – 4y + 8 = 0
7x + 6y – 9 = 0
Answer:
We have,
5x – 4y + 8 = 0
7x + 6y – 9 = 0
Here, a1 = 5, b2 = -4, c1 = 8
a1 = 7, b2 = 6, c1 = -9
∴
∴ Two line are intersecting with each at a point.
Question 2.
By comparing the ratios find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
9x + 3y + 12 = 0
18x + 6y – 24 = 0
Answer:
We have,
9x + 3y + 12 = 0
18x + 6y – 24 = 0
Here, a1 = 9, b2 = 3, c1 = 12
a1 = 18, b2 = 6, c1 = -24
∴
∴ Both the lines will coincide.
Question 3.
By comparing the ratios find out whether the lines represented by the following pairs of linear equations intersect at a point, are parallel or are coincident.
6x – 3y + 10 = 0
2x - y + 9 = 0
Answer:
We have,
6x – 3y + 10 = 0
2x - y + 9 = 0
Here, a1 = 6, b2 = -3, c1 = 10
a1 = 2, b2 = -1, c1 = 9
∴
∴ Two line are parallel to each other.
Question 4.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
3x + 2y = 5
2x -3y = 7
Answer:
Here, a1 = 3, b2 = 2, c1 = 5
a1 = 2, b2 = -3, c1 = 7
∴
∴ two equations are consistent.
Question 5.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x - 3y = 8
4x -6y = 9
Answer:
2x - 3y = 8 4x -6y = 9
Here, a1 = 2, b2 = -3, c1 = 8
a1 = 4, b2 = -6, c1 = 9
∴
∴ both lines are inconsistent
Question 6.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
9x -10y = 12
Answer:
9x -10y = 12
Here, a1 = , b2 =
, c1 = 7
a1 = 9, b2 = -10, c1 = 12
∴
∴ both lines are consistent
Question 7.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
5x - 3y = 11
-10x + 6y = -22
Answer:
5x - 3y = 11 -10x + 6y = -22
Here, a1 = 5, b2 = -3, c1 = 11
a1 = -10, b2 = 6, c1 = -22
∴
∴ two lines are consistent
Question 8.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x + 3y = 12
Answer:
2x + 3y = 12
Here, a1 = , b2 = 2, c1 = 8
a1 = 2, b2 = 3, c1 = 12
∴
∴ two equations are consistent
Question 9.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
x + y = 5
2x + 2y = 10
Answer:
x + y = 5 2x + 2y = 10
Here, a1 = 1, b2 = 1, c1 = 5
a1 = 2, b2 = 2, c1 = 10
∴
∴ two lines are inconsistent
Question 10.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
x - y = 8
3x + 3y = 16
Answer:
x - y = 8 3x + 3y = 16
Here, a1 = 1, b2 = -1, c1 = 8
a1 = 3, b2 = 3, c1 = 12
∴
∴ two lines are inconsistent
Question 11.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x + y =
6 4x - 2y = 4
Answer:
2x + y = 6 4x - 2y = 4
Here, a1 = 2, b2 = 1, c1 = 6
a1 = 4, b2 = -2, c1 = 4
∴
∴ two lines are consistent
Question 12.
Check whether the following equation are consistent or inconsistent. Solve them graphically.
2x - 2y =
2 4x - 4y = 5
Answer:
2x - 2y = 2 4x - 4y = 5
Here, a1 = 2, b2 = 2, c1 = 2
a1 = 4, b2 = 4, c1 = 5
∴
∴ two lines are inconsistent.
Question 13.
Neha went to a ‘sale’ to purchase some pants and skirts. When her friend asked her how many of each she had bought, she answered “The number of skirts are two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased.”
Help her friend to find how many pants and skirts Neha bought.
Answer:
Let the number of pants purchased by Neha be ‘x’ and no. of skirts purchased be ‘y’.
Twice the number of pants = 2x
From the given condition,
y = 2x – 2 (I)
i.e. number of skirts are 2 less than 2 twice the number of pants.
y = 4x – 4 (II)
i.e. number of skirts are 4 less than four times the number of pants.
Subtracting eq. I from II, we get
2x = 2
⇒ x = 1
So number of pants purchased = 1 and number of skirts = 0
Graphical Representation:Question 14.
10 students of Class-X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys then, find the number of boys and the number of girls who took part in the quiz.
Answer:
Let the number of girls and boys in the class be x and y respectively
According to given condition, we have:
x + y = 10
x-y = 4
x + y = 10 ⇒ x = 10-y x-y = 4 ⇒ x = 4 + y
From the graph it can be observed that the two lines intersect each other at the point (7, 3)
So, x = 7 and y = 3
Number of Girls = 7;
Number of boys = 3
Question 15.
5 pencils and 7 pens together cost D50 whereas 7 pencils and 5 pens together cost D46. Find the cost of one pencil and that of one pen.
Answer:
Let the cost of one pencil and one pen be ₹x and ₹y respectively.
According to given situation, we have :
5x + 7y = 50
7x + 5y = 46
5x + 7y = 50 7x + 5y = 46
From the graph. It can be observed that the two lines are intersecting each other at (3,5)
x = 3 and y = 5
Cost of pencil = ` 3;
Cost of pen = ` 5
Question 16.
Half the perimeter of a rectangular garden is 36 m. If the length is 4m more than its width, is 36 m. Find the dimensions of the garden.
Answer:
Let l be the length and b be the breadth
l = b + 4
l-b = 4
Perimeter = 2(l + b)
× 2(l + b) = 36 (given)
l-b = 4 ……I
l + b = 36 ….II
adding eq. I and II
⇒ 2l = 40
⇒ l = = 20m
Substitute l = 20 in(1)
l-b = 4
20-b = 4
b = 20-4 = 16m
Length = 20 m
Width = 16 m
Question 17.
We have a linear equation 2x + 3y-8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.
Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.
Answer:
2x + 3y-8 = 0
3x + 2y-7 = 0(intersecting)
2x + 3y + 12 = 0 (parallel lines)
4x + 6y-16 = 0 (coincident lines)
Question 18.
The area of a rectangle gets reduced by 80 sq uints if its length is reduced by 5 units and breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area will increase by 50 sq units. Find the length and breadth of the rectangle.
Answer:
Let the length be x and breadth be y
According to question,
xy-80 = (x-5)(x + 2)
⇒xy-80 = xy + 2x-5y-10
⇒-80 + 10 = 2x-5y
⇒ 2x-5y = -70 ….I
(x + 10)(y-5) = xy + 50
⇒ xy-5x + 10y-50 = xy + 50
⇒ -5x + 10y = 100
⇒ -x + 2y = 20 ….II
Multiplying Eq. II by 2
2x-5y = -70
-2x + 4y = 40
-y = -30
y = 30
substituting y = 30 in eq. II
-x + 2× 30 = 20
-x = 20-60
x = 40
length = 40units and breadth = 30 units
Question 19.
In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.
Answer:
Let the number no. of students be x
Let the number no. of benches be y
According to given condition, we have
x = 3y + 1 ⇒ x-3y = 1 …..I
x = 4(y-1) ⇒ x = 4y-4 ⇒ x-4y = -4 ….II
Equating eq. I and II
x-3y = 1
-x + 4y = 4
y = 5
Substituting y = 5 in eq. I
x-3×5 = 1
⇒ x-15 + 1 ⇒x = 16
Number of students = 16;
Number of benches = 5
Exercise 4.2
Question 1.The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save D2000 per month, find their monthly income.
Answer:Let the monthly incomes be represented by x and their expenditure be represented by y.
According to the given income ratios,
Income of the first person is 9x and that of the second persons is 7x.
According to the given expenditure ratios;
Expenditure of the first person is 4y and the second person’s is 3y.
Both of them manage to save ₹2000 per month.
i.e. income – expenditure = savings
Then,
9x – 4y = 2000 …I
7x - 3y = 2000 …II
Multiplying I by 3 and II by 4, we get
27x – 12y = 6000 …III
28x – 12y = 8000 …IV
Subtracting III from IV, we get
x = 2000
Putting x = 2000 in I we get,
18000 – 4y = 2000
⇒ 16000 = 4y
⇒ y = 4000
Now,
Income of the first person = 9x = 9× 2000 = 18000
Income of the second person = 7x = 7× 2000 = 14000
Question 2.The sum of a two digit number and the number obtained reversing the digits is 66. If the digits of the number differ by 2, find the number. how many such numbers are there?
Answer:Let the digit in the unit’s place be x and the digit in the tens place be y.
Then, the number = 10y + x
The number obtained by reversing the order of the digits = 10x + y
According to given conditions,
(10y + x) + (10x + y) = 66
⇒ 11(x + y) = 66
⇒ (x + y) = 6
According to second situation, digits differ by 2
So, either x – y = 2 or y – x = 2
Thus , we have the following sets of simuntaneous equations
x + y = 6 …I
x – y = 2 …II
or,
x + y = 6 …III
x – y = 2 …IV
solving equation I and II, we get x = 2 and y = 4
solving equation III and IV , we get x = 4 and y = 2
When x = 4 and y = 2,
Two digit number = (10y + x) = 10(4) + 2 = 42
When x = 2 and y = 4,
Two digit number = (10y + x) = 10(2) + 4 = 24
Hence, the required number is either 24 or 42.
Question 3.The larger of two supplementary angles exceeds the smaller by 18o. Find the angles.
Answer:Let the larger of the two supplementary angles be ‘y’ and the smaller angle be ‘x’
Therefore, x + y = 180 …I
(∵ sum of supplementary angles is 180° )
Also, y = x + 18 (∵ Given) …..II
Substituting II in I, we get,
x + x + 18 = 180
⇒ 2x + 18 = 180
⇒ 2x = 180 – 18
⇒ 2x = 162
⇒ x = 81°
Substitute x = 81 in II
y = 81 + 18 = 99°
Therefore, measure of larger angle is 99° and the measure of the smaller angle is 81°
Question 4.The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. For a distance of 10 km., the charge paid is D220. For a journey of 15km. the charge paid is D310.
i. What are the fixed charges and charge per km?
ii. How much does a person have to pay for travelling a distance of 25 km?
Answer:i. Let the fixed charge be x.
Let the charges per km be y.
Total charges to be paid will be the sum of the fixed charges and the charges per km.
For 10kms, the amount paid is ₹220.
x + 10y = 220 …I
For 15kms, the amount paid is ₹ 310
x + 15y = 310 …II
Solving I and II we get
x + 10y = 220
x + 15y = 310
- - -
-5y = -90
y = 18
Substituting the value of y in Eq. I we get
x + 10(18) = 220
x = 220 – 180
x = 40
The Fixed charge are ₹ 40 and the charges per km are ₹18
ii. For 25 km ,
total = 40 + 25(18) = 40 + 450 = 490
hence, for 25 km, the taxi fare is 490
Question 5.A fraction becomes equal to
if 1 is added to both numerator and denominator. If however, 5 is subtracted from both numerator and denominator, the fraction becomes equal to
What is the fraction?
Answer:Let the numerator be x and denominator be y.
Hence, the fraction = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAfCAMAAAAcCScXAAAAAXNSR0IArs4c6QAAAGZQTFRFAAAAAAAAAAA6ADo6ADpmADqQAGaQAGa2OgAAOjoAOma2OpDbZgAAZgA6ZjpmZpDbkDoAkDpmkLb/kNv/tmYAtmY6ttv/tv//25A625Bm27Zm2////7Zm/7aQ/9uQ/9u2//+2///bEr9S1wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQYV42M2wqAIBBER8uy+0Ury7L8/59stbcgaGBYDnNY4JVNcuWkAHZhTWlpNUkXnbUQAY/R9+mMVeZeM/J+hj35aX9rmnG105+zroCJaoT1wwJcjTKEgM5aQsDJiLgiTirItLIynBsscQTKorYtrAAAAABJRU5ErkJggg==)
Then, according to first condition, we have
and
⇒ 5x + 5 = 4y + 4
⇒ 5x – 4y = -1 ….I
According to second condition,
![](data:image/png;base64,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)
⇒ 2x – 10 = y – 5 …II
Using the elimination method, multiplying eq. I by 2 and Eq. II by 5
10x – 8y = -2
10x – 5y = 25
- + - _
-3y = -27
y = 9
substitute the value of y = 9 in Eq. I
5x – 4(9) + 1 = 0
5x = -1 + 36
x = 7
hence, the given fraction is
.
Question 6.Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time at different speeds. If the cars travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer:Let the speed of faster car = x km/h
Speed of slower car = y km/h
Relative speed when both car travels in same direction = x-y
If the cars travel in the same direction, they meet in 5 hours.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAI0AAAApCAMAAAA/DVpvAAAAAXNSR0IArs4c6QAAAJ9QTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmY6OmaQOma2OpDbZgAAZjoAZjo6ZmY6ZpC2ZpDbZrbbZrb/kDoAkDo6kGYAkLyQkLbbkNvbkNv/tmYAtmY6tmZmtpA6trZmttvbttv/tv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///bbE98kgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACjElEQVRYR+1YaXfaMBDUmoS4CW0IOZ2kBEgPIAe24///2zq7umx4waljGfpe9UHaZ2RpvBppNCj1v3SYgZQo6XC6uqlSRiPVPpQsXkeTfZnsDJigqZQ02g2a7JzoG9Bo8uR3RNFwNSOU3rx4OiYa8iJSsow5Uor7R+iJNrpuO39ZfKOKewbCCSpu+6vivr9Skpvi9mhVTDnK4sFELXSvG5WPEmmfN1L6WXRTTK0JzGjeRmcIvho0Mrasoqnwo/RH4RZoPzt99X2ZvjTjjAa/uIfnjUfDfXV/ZdppPywaBaYczi2a4vkiFjoJpCoaZhb1AqNRYAPy73hTyttmbtrFIkTldbHfz5QRSggaqaorZanSOmX0hy2iscov7FksO+YcALP4TD1+R5VfupORn2FjYQ8+TvABaJdtb/FihvPlJaYkY4bkd6hPedfgcYKKhq8j89vbiAhwcO4cjtEBbXSl99c/WPZRmvcmjZtiuEtonaAxOptS9PDDC6sWVKesVppDZ8PrLA1+qyfedU5QK4GW5sDF6yxPxti8oDpl9dJs0UxFWLi0e5FyOiufjnm1sG4GH+CNg9gwwLxWZwXNojfnU1LuaqXAXRQCrxQPr3W2mhs8trcPE1RyE2ilvM5q3hz5O5hT1pI0B86N09mUQOClSL8VVBd4aQ6MxulsSicxHbCeekG1yuqkOTAYP3wwc9ho4EYvbc+VtpiNBm700nY0zS2mXNbapYW2mD95XGcvSx6zfW/5kdyYi7nYy8EYV2csXxhv+RdoxEeJJiMK4i1rVlbzpmx2y5bY2d52+fHuaFvQGCnsCIhMU5ObLqFsQxPIW9acfmwxJ/5vQMNiUDmMt6xJNltMOcjWqve85R+TDlerU1FPrAAAAABJRU5ErkJggg==)
Total distance = 100 km
x-y =
⇒ x-y = 20 …1
Relative speed when both car travels in different direction = x + y
If they travel towards each other, they meet in 1 hour.
x + y = 100 …2
Adding Eq. 1 and 2
x-y = 20
x + y = 100
2x = 120
x = ![](data:image/png;base64,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)
substituting x = 60 in eq. 2
60 + y = 100
y = 100-60
y = 40 km
Speed of the faster car = 60km/h
Speed of the slower car = 40km/h
Question 7.Two angles are complementary. The larger angle is 3o less than twice the measure of the smaller angle. Find the measure of each angle.
Answer:Let the larger of the two supplementary angles be ‘y’ and the smaller angle be ‘x’
Therefore, y = 2x – 3 …I
Given two angles are complementary.
x + y = 180°
⇒ x + (2x – 3) = 180
⇒ 3x - 3 = 180
⇒ 3x = 180 + 3
⇒ 3x = 183
⇒ x = 61°
Substitute x = 61 in I
y = 61× 2 – 3 = 122 – 3 = 119°
Therefore, measure of larger angle is 119° and the measure of the smaller angle is 61°
Question 8.An algebra textbook has a total of 1382 pages. It is broken up into two parts. The second part of the book has 64 pages more than the first part. How many pages are in each part of the book?
Answer:Let the number of pages in the first part be x and in the second part be y.
Total pages number of pages is 1382,
Hence, x + y = 1380 …I
The second part of the book has 64 pages more than the first part
y = x + 64 …II
substituting value of y in equation I
x + x + 64 = 1382
2x = 1382 – 64
2x = 1318
x = 659
substituting the value of x in equation (2),
y = 659 + 64
y = 723
the pages in the first book are 659 and the pages in the second part are 723.
Question 9.A chemist has two solutions of hydrochloric acid in stock. One is 50% solution and the other is 80% solution. How much of each should be used to obtain 100ml of a 68% solution.
Answer:Let the proportion of the first solution be represented by x and the second solution be represented by y.
First solution contains 50% solution = ![](data:image/png;base64,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)
Second solution contains 80% solution = ![](data:image/png;base64,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)
Given that together they can give 100ml of 68% solution.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
5x + 8y = 680 …I
Total percentage of solution concentration is 100%
x + y = 100 …II
Multiplying Eq. II by 5 and solving with Eq. I
5x + 8y = 680
5x + 5y = 500
-__- -____
3y = 180
y = 60
substitute in Eq. II
x + 60 = 100
x = 40
Hence, the solutions are 40 and 20ml
Question 10.Suppose you have D12000 to save. You have to save some amount at 10% and the rest at 15%. How much should be saved at each rate to yield 12% on the total amount saved?
Answer:Let the amount be invested at 10% be x and amount to be invested at 15% be y.
Total amount to be invested is ₹12000
Therefore, x + y = 12000 …I
Simple interest on ₹x at 10% for 1 year = ![](data:image/png;base64,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)
Simple interest on ₹y at 15% for 1 year = ![](data:image/png;base64,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)
Now, total amounts is to be invested at 12%
= ![](data:image/png;base64,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)
![](data:image/png;base64,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)
2x + 3y = 28800 …II
Multiplying Eq. I by 2 and solving with Eq. II
2x + 3y = 28800
2x + 2y = 12000
_- - - _
y = 4800
substitute y = 4800 in Eq. I
x + 4800 = 1200
x = 7200
Hence the amount to be invested at 10% is ₹7200 and the amount to be invested at 15% is ₹4800.
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save D2000 per month, find their monthly income.
Answer:
Let the monthly incomes be represented by x and their expenditure be represented by y.
According to the given income ratios,
Income of the first person is 9x and that of the second persons is 7x.
According to the given expenditure ratios;
Expenditure of the first person is 4y and the second person’s is 3y.
Both of them manage to save ₹2000 per month.
i.e. income – expenditure = savings
Then,
9x – 4y = 2000 …I
7x - 3y = 2000 …II
Multiplying I by 3 and II by 4, we get
27x – 12y = 6000 …III
28x – 12y = 8000 …IV
Subtracting III from IV, we get
x = 2000
Putting x = 2000 in I we get,
18000 – 4y = 2000
⇒ 16000 = 4y
⇒ y = 4000
Now,
Income of the first person = 9x = 9× 2000 = 18000
Income of the second person = 7x = 7× 2000 = 14000
Question 2.
The sum of a two digit number and the number obtained reversing the digits is 66. If the digits of the number differ by 2, find the number. how many such numbers are there?
Answer:
Let the digit in the unit’s place be x and the digit in the tens place be y.
Then, the number = 10y + x
The number obtained by reversing the order of the digits = 10x + y
According to given conditions,
(10y + x) + (10x + y) = 66
⇒ 11(x + y) = 66
⇒ (x + y) = 6
According to second situation, digits differ by 2
So, either x – y = 2 or y – x = 2
Thus , we have the following sets of simuntaneous equations
x + y = 6 …I
x – y = 2 …II
or,
x + y = 6 …III
x – y = 2 …IV
solving equation I and II, we get x = 2 and y = 4
solving equation III and IV , we get x = 4 and y = 2
When x = 4 and y = 2,
Two digit number = (10y + x) = 10(4) + 2 = 42
When x = 2 and y = 4,
Two digit number = (10y + x) = 10(2) + 4 = 24
Hence, the required number is either 24 or 42.
Question 3.
The larger of two supplementary angles exceeds the smaller by 18o. Find the angles.
Answer:
Let the larger of the two supplementary angles be ‘y’ and the smaller angle be ‘x’
Therefore, x + y = 180 …I
(∵ sum of supplementary angles is 180° )
Also, y = x + 18 (∵ Given) …..II
Substituting II in I, we get,
x + x + 18 = 180
⇒ 2x + 18 = 180
⇒ 2x = 180 – 18
⇒ 2x = 162
⇒ x = 81°
Substitute x = 81 in II
y = 81 + 18 = 99°
Therefore, measure of larger angle is 99° and the measure of the smaller angle is 81°
Question 4.
The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. For a distance of 10 km., the charge paid is D220. For a journey of 15km. the charge paid is D310.
i. What are the fixed charges and charge per km?
ii. How much does a person have to pay for travelling a distance of 25 km?
Answer:
i. Let the fixed charge be x.
Let the charges per km be y.
Total charges to be paid will be the sum of the fixed charges and the charges per km.
For 10kms, the amount paid is ₹220.
x + 10y = 220 …I
For 15kms, the amount paid is ₹ 310
x + 15y = 310 …II
Solving I and II we get
x + 10y = 220
x + 15y = 310
- - -
-5y = -90
y = 18
Substituting the value of y in Eq. I we get
x + 10(18) = 220
x = 220 – 180
x = 40
The Fixed charge are ₹ 40 and the charges per km are ₹18
ii. For 25 km ,
total = 40 + 25(18) = 40 + 450 = 490
hence, for 25 km, the taxi fare is 490
Question 5.
A fraction becomes equal to if 1 is added to both numerator and denominator. If however, 5 is subtracted from both numerator and denominator, the fraction becomes equal to
What is the fraction?
Answer:
Let the numerator be x and denominator be y.
Hence, the fraction =
Then, according to first condition, we have
and
⇒ 5x + 5 = 4y + 4
⇒ 5x – 4y = -1 ….I
According to second condition,
⇒ 2x – 10 = y – 5 …II
Using the elimination method, multiplying eq. I by 2 and Eq. II by 5
10x – 8y = -2
10x – 5y = 25
- + - _
-3y = -27
y = 9
substitute the value of y = 9 in Eq. I
5x – 4(9) + 1 = 0
5x = -1 + 36
x = 7
hence, the given fraction is .
Question 6.
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time at different speeds. If the cars travel in the same direction, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Answer:
Let the speed of faster car = x km/h
Speed of slower car = y km/h
Relative speed when both car travels in same direction = x-y
If the cars travel in the same direction, they meet in 5 hours.
Total distance = 100 km
x-y = ⇒ x-y = 20 …1
Relative speed when both car travels in different direction = x + y
If they travel towards each other, they meet in 1 hour.
x + y = 100 …2
Adding Eq. 1 and 2
x-y = 20
x + y = 100
2x = 120
x =
substituting x = 60 in eq. 2
60 + y = 100
y = 100-60
y = 40 km
Speed of the faster car = 60km/h
Speed of the slower car = 40km/h
Question 7.
Two angles are complementary. The larger angle is 3o less than twice the measure of the smaller angle. Find the measure of each angle.
Answer:
Let the larger of the two supplementary angles be ‘y’ and the smaller angle be ‘x’
Therefore, y = 2x – 3 …I
Given two angles are complementary.
x + y = 180°
⇒ x + (2x – 3) = 180
⇒ 3x - 3 = 180
⇒ 3x = 180 + 3
⇒ 3x = 183
⇒ x = 61°
Substitute x = 61 in I
y = 61× 2 – 3 = 122 – 3 = 119°
Therefore, measure of larger angle is 119° and the measure of the smaller angle is 61°
Question 8.
An algebra textbook has a total of 1382 pages. It is broken up into two parts. The second part of the book has 64 pages more than the first part. How many pages are in each part of the book?
Answer:
Let the number of pages in the first part be x and in the second part be y.
Total pages number of pages is 1382,
Hence, x + y = 1380 …I
The second part of the book has 64 pages more than the first part
y = x + 64 …II
substituting value of y in equation I
x + x + 64 = 1382
2x = 1382 – 64
2x = 1318
x = 659
substituting the value of x in equation (2),
y = 659 + 64
y = 723
the pages in the first book are 659 and the pages in the second part are 723.
Question 9.
A chemist has two solutions of hydrochloric acid in stock. One is 50% solution and the other is 80% solution. How much of each should be used to obtain 100ml of a 68% solution.
Answer:
Let the proportion of the first solution be represented by x and the second solution be represented by y.
First solution contains 50% solution =
Second solution contains 80% solution =
Given that together they can give 100ml of 68% solution.
5x + 8y = 680 …I
Total percentage of solution concentration is 100%
x + y = 100 …II
Multiplying Eq. II by 5 and solving with Eq. I
5x + 8y = 680
5x + 5y = 500
-__- -____
3y = 180
y = 60
substitute in Eq. II
x + 60 = 100
x = 40
Hence, the solutions are 40 and 20ml
Question 10.
Suppose you have D12000 to save. You have to save some amount at 10% and the rest at 15%. How much should be saved at each rate to yield 12% on the total amount saved?
Answer:
Let the amount be invested at 10% be x and amount to be invested at 15% be y.
Total amount to be invested is ₹12000
Therefore, x + y = 12000 …I
Simple interest on ₹x at 10% for 1 year =
Simple interest on ₹y at 15% for 1 year =
Now, total amounts is to be invested at 12%
=
2x + 3y = 28800 …II
Multiplying Eq. I by 2 and solving with Eq. II
2x + 3y = 28800
2x + 2y = 12000
_- - - _
y = 4800
substitute y = 4800 in Eq. I
x + 4800 = 1200
x = 7200
Hence the amount to be invested at 10% is ₹7200 and the amount to be invested at 15% is ₹4800.
Exercise 4.3
Question 1.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
Let
be p and
be q,
We get the following pair of linear equations:
5p + q = 2 …III
6p – 3q = 1 …IV
Using the elimination method:
Multiplying eq. III by 3 and adding to IV, we get
15p + 3q = 6
6p – 3q = 1
21p = 7
⇒ p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAeCAMAAAC7U6a3AAAAAXNSR0IArs4c6QAAAG9QTFRFAAAAAAAAAAA6ADo6AGaQAGa2OgAAOgA6OjoAOmZmOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDoAkDo6kDqQkGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///bzD6DNwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA2ElEQVQ4T92U3RKCIBSEFyv7VSsrDS0xef9nDBCLrOhcOE0TNzrDfiznAAt8ecgtU2NCcpXHTid3FWSaUahiHruriwUFUhruUESrHiVoVT1SdCt3h3QrmY8r2wG6FddntCQ27o9kua7bjOD5rt3m2p8PZVv10M3x7nBos59Z7xwzZt7xPRE8eytmLEiAJjqg1OfYS4TXpEytWk3XU3P6biJ47KwavH0wNOqyXxt1aeOJROVsZCjeZRqJAk7hBtBBKNQXTiK8raqJMtSKalb6HiuKlghFqDt/Bdm7ChazPHpaAAAAAElFTkSuQmCC)
Substitute the value of p in eq. III
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHkAAAApCAMAAAAmqnaMAAAAAXNSR0IArs4c6QAAAIFQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OjoAOjpmOmaQOma2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkDo6kGYAkGY6kGZmkLbbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ2////7Zm/9uQ/9u2//+2///bqnQ5dgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACHUlEQVRYR+1Y3VrDIAwF/1Z1s5uKTmVbddoy3v8BBRIYCP1k3Yo39mpraU/PSXISSsj/4SmwXbz9iR5iTs83pZHly5p003VjkLtZQfjVnQEDZIL/SuA3E0BBZMkeS6Bqea8xsRCZtKXizZGy5UwkA/XHPhxlh1yKdHP1heSs2mRXlyDtoThkwt3bjKh4e+aMq3E/vZPjQVuicllRSi/uDVJXjS+3ZClhJbP5PgLldxB5Vycxxgl0p2WlGNMeXfnpzERu55ReGp5d5bljS5NWuU82lHu4pXL6QEQNzagwsg5nYwgGyBE54BhJEXPulIiz58zmAs87DbJOEMnSsYoLAvKmq24rDLmSYW8k/vrfOZvsD5dxnbnm+PlQJCufVMgZXrTI7iYaq516IphuIF9/6QfNz1bTUM6HIIe+ZB3klMh9avMJdkMOOoEzD61n4NFzd6i7acOthuMqxIKhSQ1FVqn5SsQiI7fN5CENXbWe0ukaXizXPaN6litVzp++KfVkGMYgan6uY8iPG2uvWpe80SAzt5Pv5Lok1+rZWsvtkscgu7HPTKBgr/mTQUuPmCCCwcc2x8xpqFUJk2ncCcG9CVAsbd5lhrnftbKu2Kl3V6uMh5IvM/XuNzeEbCuo8lLbG7e70Z6kM6bU7sYnDb5SirKqJVVQwNN46fCRKyuvgkVqry61iQgzfBfcuRP9tULoPcZMARf9WnG4SkPu+AYjxC2KSXqJwwAAAABJRU5ErkJggg==)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
But,
⇒ 3 = x – 1 ⇒ x = 4
⇒ 3 = y – 2 ⇒ y = 5
So, x = 4 and y = 5
Question 2.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
![](data:image/png;base64,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)
⇒
…I
⇒ ![](data:image/png;base64,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)
Substituting
= p and
= q
We get the pair of linear equation,
p + q = 2 …III
p – q = 6 ….IV
using the elimination method,
p + q = 2
p – q = 6
2p = 8
p = 4
substitute the value of p in Eq. III
4 + q = 2
q = -2
but,
= p = 4 ⇒ x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAABmADqQAGaQAGa2OgAAOjoAOmZmOma2OpDbZjoAZjpmZrbbZrb/kDoAkDo6kGaQtmYAtmY6tv//25A625Bm29uQ2////7Zm/9uQ//+2///bTz76BgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQYV2NgwAAywqwgMTEObjDNwCCKn5YRYpEAqWIEAi5M43CIgFQDAdHqkRRKsfGBeDIC7GBalJcfREtyyoBoaR4RGX5eQYhzGJnBCsHyDAzibEwiADC6A1V8bn48AAAAAElFTkSuQmCC)
= q = -2 ⇒ x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAeCAMAAAAB8C7XAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQoU2NgoAKQFGDBaooQGzd2CQYGQdpLSPIzi2JzliAjEHBQwdsUGcEPcgUYMPEBDYKyKTKSnppFuBkZ2bFYKMHFyyAM9hEWIM6KQ0IQR3QIY7MCaLAgDnExoLgYD6bNEpyg8OVhAAAkxwKUHdR+TgAAAABJRU5ErkJggg==)
Question 3.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:
and ![](data:image/png;base64,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)
Let
be p and
be q
2p + 3q = 2 …III
4p – 9q = -1 …IV
Multiplying eq. III by 3 and subtracting with eq. IV, we get
6p + 9q = 6
4p – 9q = -1
10p = 5
p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADUAAAAfCAMAAABwD3USAAAAAXNSR0IArs4c6QAAAGNQTFRFAAAAAAAAAAA6ADqQAGaQAGa2OgAAOgA6OmZmOma2OpDbZgAAZgA6ZjoAZpDbZrbbZrb/kDoAkDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bvX5P1wAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA0klEQVQ4T9WU2w6DIAyGi5s7KRs7iMyp8P5PuSIHs2SRungxuSKhX/sX6A+wjqUYY1lF0mrqPMQpQSIw6HngP1AAaqRQ4ZFYbqQQ6HdElR+UuZ5oxSJlbhW5lpHb1qU3NV78hVTKvhEjqiIlXEmQtH0P68sPjWduk2jJRy/d+KTCpYv9Tz7vBObOsnNS1Yu7+Q1OoPK236ccR5cPaNyrD3OmCwG0yfS5HVViBhmdZEKqcuM1j2q8Lc1SqDzknUBuCLcBHUIdullwAs0J3qEL++vFGwuQCfOvLvcKAAAAAElFTkSuQmCC)
substitute value of p in Eq. III
+ 3q = 2
⇒ 3q = 2 – 1
⇒ q = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6ADo6AGaQAGa2OgAAOgA6OjoAOmZmOpDbZgA6ZjoAZpDbZrbbZrb/kDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ2////9uQ/9u2//+2///bjLFCZQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWklEQVQYV42MSw6AIAwFH6j4FxUUFeX+x5R24YZofJtJJtMCycJSkHN1xwTWbwabH1SJuCZ992KojvvdP6GrhOyBMM7YpGHtS+Y5DQQrMiawK42rNfCRcIrubjqJA0n8PQVyAAAAAElFTkSuQmCC)
But,
⇒
⇒
⇒ x = 4
⇒
⇒
⇒ y = 9
Question 4.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:6x + 3y = 6xy
2x + 4y = 5xy
⇒
….I
⇒
….II
Let
= p and
= q
6p + 3q = 6
2p + 4q = 5
Multiplying eq. IV by 3 and subtracting from Eq. III
6p + 3q = 6
6p + 12q = 15
-9q = -9
q = 1
substitute the value of q in III
6p + 3(1) = 6
p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQYV2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PAPT8AmzwjKRVAAAAAElFTkSuQmCC)
But,
⇒ x = 2
⇒ y = -1
Question 5.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:
and ![](data:image/png;base64,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)
Let
= p and
= q
5p – 2q = -1 ….I
15p + 7q = 10 ….II
Multiply Eq. I by 3 and subtract eq. II
15p – 6q = -3
-15p - 7q = -10
-13q = -13
q = 1
substitute the value of q in Eq. I
5p – 2(1) = -1
⇒ 5p = - 1 + 2
⇒ 5p = 1
⇒ p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOmZmOma2OpDbZjoAZrbbZrb/kDoAkDo6kNv/tmYAtmY625A625Bm2////9uQ///b7M5aaQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQYV2NgwACiAiwgMSE2TjDNwCCInxblZxYGqWIEAg5M43CIgFQDAdHq4QpB9jDxAe3jhroORgPF2SFCIqwQMVEeDgZRXj4wX1QAqI2LAQDhjwJMpG7StAAAAABJRU5ErkJggg==)
But,
⇒ 5 = x + y …III
⇒ 1 = x – y ⇒ y = x – 1
Substitute value of y in eq. III
x + x – 1 = 5
⇒ 2x = 6
⇒ x = 3
∴ y = 3 – 1 = 2
x = 3 and y = 2
Question 6.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF8AAAA7CAMAAAAq96aLAAAAAXNSR0ICQMB9xQAAAWJQTFRFgYGBAAAAqgAAAACqAAAAAAAAiIhmZoiId3dmZnd3ZmZVboBuf39dXX9/d3ddXXd3d3dVVXd3f25ZWW5/e2pVd2pVVWp3gHNIf25ISG5/e2pERGp7ampVVWpqRGp7SFtxgF0zM12AgFszRldqM1uAf1kzM1l/fVkxbls1bFkzNUhubkgdHUhuHUhqbEYdHUZsbEYdHUZsSDNIRkYzHUhbMzNbNDRIMzNIWzMdHTNbHTNZWjMdHTJaHTJYSDQeMx5HWjMAWzMAADNbADNZWjMAWTMAADJaADJYNB00NDQdSR0dHR1JSB0dADNIADNGHh40SR0ARx0AAB1JMwAzSB0AAB1ISBwARhwAABxGHR0dMx0AAB0zMx0AHQAzMh0AAB0yMh0AAB0yAB4eHh4AHR0AMwAAAAAzMwAAAAAzAAAzHQAAAAAdHQABHQAAHQAAAAAdAAAAAAAAAQAAAAABAAAAAAAAUr+A2gAAAHV0Uk5TAAECAgIDDAwNDQ4YGRkaGhsbJSUmJycwMTEyMjMzM0lLS0xMTE1NTldaY3JycnNzdHR8fn5+iouMjIyNjo6Ymp+goKChoaKip6ioqKmurrW6urq6u7u8vb3DyMjJycrKy8vX2Nnb29zc3erq6+vs7Pz9/v7+chlt9AAAAlJJREFUeNrtl+tbEkEUxs/QuCsEVpAGG5VYXpIV2K6WplFamV2oiMhuUilBCc628//3zFZL2MPMcja+GO+H5cuZ3549c3jnDMBQ/4UopZSoQ7D48W3Oa+elLzi5xdiHCRze2GOM2XxGFnJNh/jbRgyD18pXdIiXbMlq7ZIOAMnWBQw/Oe8iKu2U6ju/ZQLs8doXxdfT9TsB8FpFvjqU3n4cDsA33knT154xxpfxLyBLqtpqc01uofE500cj7OEaFACm5n21AJJPjKvujyqu8FJH4WeXhbuMX9cl7gMAoxUThb/Y4q56r47Xa2doZPEGqjpz7Ke+9v7/aiuMsafn5Gn+duAgTtubnr78Of/LaffRTttbkx8/8bzntFuNY6p8SN8t7vL9Om0uj+P7ddpAfLp+F4LxCfVEDvJD6fdPwgH5WebJPMB3nfZW+M+5oCMvt4LVye3vEHl9upyWdcnLzXHEM9MjRLW/p5ROG6D+QsWAfEn9/Tktpj+tjtOWF/51/9NZfn+EuE47Elm8qQrP9mn1yaao1QJoK/tKpx3q8N1d5GcmpfQIQEg8+lV0x+bfzWidS4736A7nz3Wt5GDmH61oV8MwvZuQxMTrwk/GXiRQk3mJz0Qeyi8XWXF7Kpi4HYjWGxsZVcg90B6lkFs85VRVB1qxfdrY1JH86de2arJPtixsecDYPFpun1VdMmsbyPIcfxATV4cTigHNxg3nMPrKIkAKvDqhuP8hy3NbHHFZ+fwstJQaqI2MreqDgxNK0d3jRznu7MYGyJ9svknAUEN16wdeR39tjTOamAAAAABJRU5ErkJggg==)
![](data:image/png;base64,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)
Answer:
and ![](data:image/png;base64,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)
Let
= p and
= q
2p + 3q = 13 …I
5p – 4q = -2 …II
Multiply Eq. I by 4 and Eq. II by 3 and solve
8p + 12q = 52
15p – 12q = -6
23p = 46
P = 2
Substitute the value of p in Eq. I
2(2) + 3q = 13
⇒ 4 + 3q = 13
⇒ 3q = 9
⇒ q = 3
But,
= p = 2 ⇒ x = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQYV2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PAPT8AmzwjKRVAAAAAElFTkSuQmCC)
= q = 3 ⇒ y = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAF1QTFRFAAAAAAAAAAA6ADo6AGaQAGa2OgAAOgA6OjoAOmZmOpDbZgA6ZjoAZpDbZrbbZrb/kDo6kGY6kLbbkNv/tmYAtmY625A625Bm27Zm27aQ2////9uQ/9u2//+2///bjLFCZQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWklEQVQYV42MSw6AIAwFH6j4FxUUFeX+x5R24YZofJtJJtMCycJSkHN1xwTWbwabH1SJuCZ992KojvvdP6GrhOyBMM7YpGHtS+Y5DQQrMiawK42rNfCRcIrubjqJA0n8PQVyAAAAAElFTkSuQmCC)
Question 7.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:
and ![](data:image/png;base64,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)
Let
= p and
= q
10p + 2q = 4 …I
15p – 5q = -2 …II
Multiply Eq. I by 5 and Eq. II by 2
50p + 10q = 20
30p – 10q = -4
80p = 16
p = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AGaQAGa2OgAAOmZmOma2OpDbZjoAZrbbZrb/kDoAkDo6kNv/tmYAtmY625A625Bm2////9uQ///b7M5aaQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAUklEQVQYV2NgwACiAiwgMSE2TjDNwCCInxblZxYGqWIEAg5M43CIgFQDAdHq4QpB9jDxAe3jhroORgPF2SFCIqwQMVEeDgZRXj4wX1QAqI2LAQDhjwJMpG7StAAAAABJRU5ErkJggg==)
substitute value of p in eq. I
10
+ 2q = 4
⇒ 2 + 2q = 4
⇒ 2q = 2
⇒ q = 1
But,
⇒ 5 = x + y …III
⇒ 1 = x – y ⇒ y = x – 1
Substitute value of y in eq. III
x + x – 1 = 5
⇒ 2x = 6
⇒ x = 3
∴ y = 3 – 1 = 2
x = 3 and y = 2
Question 8.Solve each of the following pairs of equations by reducing them to a pair of linear equation.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Answer:
and ![](data:image/png;base64,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)
Let
= m and
= n
m + n
⇒ 4(m + n) = 3 ⇒4m + 4n = 3…(I)
⇒ 8(m-n) = -1 × 2 ⇒8m-8n = -2…(II)
Multiply Eq. I by 2
8m + 8n = 6
8m - 8n = -2
16m = 4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Substituting
in Eq. II
– 8n = -2
⇒ 2 – 8n = -2
⇒ -8n = -4
⇒ n = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAcAAAAeCAMAAADXVfSyAAAAAXNSR0IArs4c6QAAAE5QTFRFAAAAAAAAAAA6AGaQAGa2OgA6OmZmOma2OpDbZgAAZgA6ZjoAZrb/kLbbkNv/tmYAtmY625A625Bm27Zm29u22////7Zm/9uQ//+2///bgWo6oAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAV0lEQVQYV2NgwACSAiwgMSE2bjDNwCCIn5bkZxYFqWIEAg5M43CIgFQDAdHq4QpFuBkZ2RkYJLh4GYSZ+MDC4qwQWhBivTBQGsSDUGJASoyHQYITZB0PAPT8AmzwjKRVAAAAAElFTkSuQmCC)
∴
⇒
⇒ 4 = 3x + y ⇒ 4 = 3x + y ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACkAAAAVBAMAAAAp9toTAAAAAXNSR0IArs4c6QAAACpQTFRFAAAAAAAAAABmAGa2OgAAOpDbZgAAZrb/kDoAtv//25A6/9uQ//+2///bZHgkawAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAN0lEQVQoU2NgGCjA2ygMQagOOGbAAEEo4IYBAwQNYlHepgkLC7YEMPAkM0C9APIFkigOH1MxAgAV2CmRvSj97gAAAABJRU5ErkJggg==)
∴
⇒
⇒ 2 = 3x-y ⇒ 2 = 3x-y ….IV
Equating Eq. III and IV
3x + y = 4
3x-y = 2
6x = 6
x = 1
Substituting x = 1![](data:image/png;base64,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)
3×1 + y = 4
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Hence, x = 1 and y = 1
Question 9.Formulate the following problems as a pair of equation and then find their solution.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Answer:Let the speed of the boat in still water be x km/h and speed of the stream be y km/h
Speed of boat upstream = (x – y) km/h
Speed of boat downstream = (x + y) km/h
But, total time of journey is 10hrs.
= 10
= 13
Let
be a and
be b
30a + 44b = 10 …I
40a + 55b = 13 …II
Multiply Eq. I by 4 and Eq. II by 3
120a + 176b = 40
120a + 165b = 39
_- - - _
11b = 1
b = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeBAMAAAABcllHAAAAAXNSR0IArs4c6QAAACdQTFRFAAAAAAAAAGaQAGa2OmZmOpDbZjoAtmYAtmY625A625Bm2//////bcdiRUwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAQklEQVQoU2NgwAZOGEBEudygDAZOIhjHtSG6OAUFA7Aai0dQEAIESNUHUw9yMQiDXAxxNcjFYFfjYYBcDMIgF4MwAJhHC+NTnMR/AAAAAElFTkSuQmCC)
substituting value of b in Eq. I
30a + 44×
= 10
⇒ 30a + 4 = 10
⇒ 30a = 6
⇒ a = ![](data:image/png;base64,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)
∴
⇒
⇒ 5 = x + y ⇒ 5 = x + y ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACkAAAAVBAMAAAAp9toTAAAAAXNSR0IArs4c6QAAACpQTFRFAAAAAAAAAABmAGa2OgAAOpDbZgAAZrb/kDoAtv//25A6/9uQ//+2///bZHgkawAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAN0lEQVQoU2NgGCjA2ygMQagOOGbAAEEo4IYBAwQNYlHepgkLC7YEMPAkM0C9APIFkigOH1MxAgAV2CmRvSj97gAAAABJRU5ErkJggg==)
∴
⇒
⇒ 11 = x - y ⇒ 11 = x - y ….IV
x + y = 5
x – y = 11
2x = 16
x = 8
substitute value of x in Eq. III
8 + y = 5
Y = 3
Hence, Speed of boat = 8 km/h;
Speed of stream = 3 km/h
Question 10.Formulate the following problems as a pair of equation and then find their solution.
Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car.
Answer:Let the speed of the train be x km/h and that of the car be y km/h
Also, we know that time = ![](data:image/png;base64,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)
In situation 1, time spent travelling by train =
h
And time spent travelling by car =
h
So, total time taken in 8hour journey is
= ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHMAAAAhCAMAAADd22QoAAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGaQAGa2OgAAOgA6OjoAOmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZpDbZrbbZrb/kDoAkDo6kDpmkGY6kGaQkLbbkLb/kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/7aQ/9uQ/9u2//+2///bKG7UHAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABxUlEQVRIS+1X23KCMBANtCKpLV6wSC/WWCNtQ5H8/9d1N6ijVskGHF7aM6NxNLsnZy9hZezPQC9D1PoVe14Eq37x/Eeb+ILPYMsGTB4U0eTQ5fo+Rs5yMmeZv2BMhqq4g7UO+mkAnDodsc14RDM5cSeNTgByleOZcVYLmaTAiVuZCGkmlzglUJUT0AiO6pBHGjl1GqkN8FJMTt3tdGaYToKDcrrSafKqTD4jRTH5pWDLKZGSEijpIQJVxglobRRbLfpQeywHyhwTFNhrCKhgZ8ErTprJoVRz6hHowxUrI/b8xNYrn/xmxVjGq14hmcD2gUdow4raiGoPiVIykEfBdThNFkweuuesb8Pdea6jk+UexhavOgJcOYXpJcQxwQeUnPlm//vRh/1JztlbTC6pKDiUj8TWIMBV53mXOsXqqd7tcOU8H9tyXNUtNrYdrpx1OrvtFUjlUHV8J1R3X29uj+v/jvYRyLi/KDitd7ZsAi6V3Dz+miIPlIQ5wwFm5FvCqznkrXWqPXEuA6WfSR1+6VTrgVNkwQ2MazgpNsf3m0577272oj9tI3PNQy1glnMiNU+KjgGDbseMy0W7om1yXGH+xjXADzGoKNN8jAMyAAAAAElFTkSuQmCC)
⇒
…I
Again, when he travels 200km by train and rest by car
Time taken by him travel 200km by train =
h
And time spent travelling by car =
h
Total time taken = ![](data:image/png;base64,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)
But given time of journey is 8hrs 20 min i.e
=
h
So,
…II
Let
= a and
= b
30a + 120b = 2 …III
200a + 400b =
…IV
Multiply Eq. III by 20 and Eq. IV by 3
600a + 2400b = 40
600a + 1200b = 25
_- - - _
1200b = 15
b = ![](data:image/png;base64,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)
substitute value of b in Eq. III
30a + 120 ×
= 2
a = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeCAMAAADEgrRGAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6ADqQAGaQAGa2OgAAOgA6Ojo6OmZmOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZpDbZrbbZrb/kDoAkGY6kNv/tmYAtmY625A625Bm27Zm29u229vb2////9uQ/9u2//+2///boIbSEAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAhUlEQVQoU6WQ2RKDMAhFQY2txiW2LjG2jQ3//4+indH4pvXO8HDDAQIAh0S98LkhUTsPYK550pH1Bhhk5Yd+dhaaO3s6W/4P/6pSXo5aDB5cTn22rGqEHW/dejlX1EBNzpFWd+ZdyTktYIzl592I1S/vJrQbLy1xHnT46/dViJInOIXBEybvnwhb+HIcXQAAAABJRU5ErkJggg==)
but,
⇒ x = 60
⇒ y = 80
Speed of train = 60 km/h
Speed of car = 80 km/h
Question 11.Formulate the following problems as a pair of equation and then find their solution.
2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.
Answer:Let the time taken by one woman to finish the work = x days
Work done by one women in one day =
days
Let the time taken by one man to finish the work = y days
Work done by one men in one day =
days
Now, 2 women and 5 men can finish the work in 4 days
So,
⇒
…I
Also, 3 women and 6 men can finish the work in 3 days
So,
⇒
…II
Let
be a and
be b
8a + 20b = 1 …III
9a + 18b = 1 …IV
Multiplying Eq. III by 9 and Eq. IV by 8 and solving
72a + 180b = 9
72a + 144b = 8
_- - - _
36b = 1
b = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeCAMAAADEgrRGAAAAAXNSR0IArs4c6QAAAHhQTFRFAAAA///b//+22////9u2/9uQ29vb29u2kNv/27aQ27ZmkLbbZrb/Zrbb25Bm25A6ZpDbOpDbOpC2tmY6tmYAkGY6Oma2OmaQOmZmkDo6AGa2kDoAAGaQZjo6ZjoAOjo6OjoAADqQADo6ZgA6OgA6OgAAAAA6AAAABhIsmwAAAAF0Uk5TAEDm2GYAAACCSURBVHjatZDbDoIwEERnLVVEqDdslQpey/z/H5pCTMqbieG87E5mNptd4Cfk2KTSnLtmGtj+p6W+qtQlyT3mgFMwO+bOfjd0ResU5LJB0efxpYfvyfqdpx/JThUg3rU3FxM1nxWgg12u/JhZhxKLV5x5DFWHEuKtkuibMO7LOtKqD3XHCi/2Bd2hAAAAAElFTkSuQmCC)
substituting value of b in Eq. III
8a + 20 ×
= 1
288a + 20 = 36
288a = 16
a = ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAAeCAMAAADEgrRGAAAAAXNSR0IArs4c6QAAAEhQTFRFAAAAAAAAAGaQAGa2OgAAOmZmOmaQOma2OpDbZgAAZjoAZrbbZrb/kDoAtmYAtmY625A625Bm27Zm2////9uQ/9u2//+2///b77fSgwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAcUlEQVQoU6WQyxKAIAhFsSwfpVlm/P+fpqQzttNid52DwAFoKtzGmtsn/coA7l9GO/hqgGOxZNNmvVD6uare9g98dhc0Y3M8MrtDIyEoupHcXWoFsGSRMhrhQ3orblO/IEkPr5fIEEnuTp5zcXfwNO8GOrYEJHY8inAAAAAASUVORK5CYII=)
⇒ x = 18
⇒ y = 36
Number of days by man = 18;
Number of days by woman = 36
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
Let be p and
be q,
We get the following pair of linear equations:
5p + q = 2 …III
6p – 3q = 1 …IV
Using the elimination method:
Multiplying eq. III by 3 and adding to IV, we get
15p + 3q = 6
6p – 3q = 1
21p = 7
⇒ p =
Substitute the value of p in eq. III
⇒
⇒
But, ⇒ 3 = x – 1 ⇒ x = 4
⇒ 3 = y – 2 ⇒ y = 5
So, x = 4 and y = 5
Question 2.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
⇒
…I
⇒
Substituting = p and
= q
We get the pair of linear equation,
p + q = 2 …III
p – q = 6 ….IV
using the elimination method,
p + q = 2
p – q = 6
2p = 8
p = 4
substitute the value of p in Eq. III
4 + q = 2
q = -2
but, = p = 4 ⇒ x =
= q = -2 ⇒ x =
Question 3.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
and
Let be p and
be q
2p + 3q = 2 …III
4p – 9q = -1 …IV
Multiplying eq. III by 3 and subtracting with eq. IV, we get
6p + 9q = 6
4p – 9q = -1
10p = 5
p =
substitute value of p in Eq. III
+ 3q = 2
⇒ 3q = 2 – 1
⇒ q =
But, ⇒
⇒
⇒ x = 4
⇒
⇒
⇒ y = 9
Question 4.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
6x + 3y = 6xy
2x + 4y = 5xy
⇒
….I
⇒
….II
Let = p and
= q
6p + 3q = 6
2p + 4q = 5
Multiplying eq. IV by 3 and subtracting from Eq. III
6p + 3q = 6
6p + 12q = 15
-9q = -9
q = 1
substitute the value of q in III
6p + 3(1) = 6
p =
But, ⇒ x = 2
⇒ y = -1
Question 5.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
and
Let = p and
= q
5p – 2q = -1 ….I
15p + 7q = 10 ….II
Multiply Eq. I by 3 and subtract eq. II
15p – 6q = -3
-15p - 7q = -10
-13q = -13
q = 1
substitute the value of q in Eq. I
5p – 2(1) = -1
⇒ 5p = - 1 + 2
⇒ 5p = 1
⇒ p =
But, ⇒ 5 = x + y …III
⇒ 1 = x – y ⇒ y = x – 1
Substitute value of y in eq. III
x + x – 1 = 5
⇒ 2x = 6
⇒ x = 3
∴ y = 3 – 1 = 2
x = 3 and y = 2
Question 6.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
and
Let = p and
= q
2p + 3q = 13 …I
5p – 4q = -2 …II
Multiply Eq. I by 4 and Eq. II by 3 and solve
8p + 12q = 52
15p – 12q = -6
23p = 46
P = 2
Substitute the value of p in Eq. I
2(2) + 3q = 13
⇒ 4 + 3q = 13
⇒ 3q = 9
⇒ q = 3
But, = p = 2 ⇒ x =
= q = 3 ⇒ y =
Question 7.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
and
Let = p and
= q
10p + 2q = 4 …I
15p – 5q = -2 …II
Multiply Eq. I by 5 and Eq. II by 2
50p + 10q = 20
30p – 10q = -4
80p = 16
p =
substitute value of p in eq. I
10 + 2q = 4
⇒ 2 + 2q = 4
⇒ 2q = 2
⇒ q = 1
But, ⇒ 5 = x + y …III
⇒ 1 = x – y ⇒ y = x – 1
Substitute value of y in eq. III
x + x – 1 = 5
⇒ 2x = 6
⇒ x = 3
∴ y = 3 – 1 = 2
x = 3 and y = 2
Question 8.
Solve each of the following pairs of equations by reducing them to a pair of linear equation.
Answer:
and
Let = m and
= n
m + n⇒ 4(m + n) = 3 ⇒4m + 4n = 3…(I)
⇒ 8(m-n) = -1 × 2 ⇒8m-8n = -2…(II)
Multiply Eq. I by 2
8m + 8n = 6
8m - 8n = -2
16m = 4
Substituting in Eq. II
– 8n = -2
⇒ 2 – 8n = -2
⇒ -8n = -4
⇒ n =
∴ ⇒
⇒ 4 = 3x + y ⇒ 4 = 3x + y
∴ ⇒
⇒ 2 = 3x-y ⇒ 2 = 3x-y ….IV
Equating Eq. III and IV
3x + y = 4
3x-y = 2
6x = 6
x = 1
Substituting x = 1
3×1 + y = 4
Hence, x = 1 and y = 1
Question 9.
Formulate the following problems as a pair of equation and then find their solution.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Answer:
Let the speed of the boat in still water be x km/h and speed of the stream be y km/h
Speed of boat upstream = (x – y) km/h
Speed of boat downstream = (x + y) km/h
But, total time of journey is 10hrs.
= 10
= 13
Let be a and
be b
30a + 44b = 10 …I
40a + 55b = 13 …II
Multiply Eq. I by 4 and Eq. II by 3
120a + 176b = 40
120a + 165b = 39
_- - - _
11b = 1
b =
substituting value of b in Eq. I
30a + 44× = 10
⇒ 30a + 4 = 10
⇒ 30a = 6
⇒ a =
∴ ⇒
⇒ 5 = x + y ⇒ 5 = x + y
∴ ⇒
⇒ 11 = x - y ⇒ 11 = x - y ….IV
x + y = 5
x – y = 11
2x = 16
x = 8
substitute value of x in Eq. III
8 + y = 5
Y = 3
Hence, Speed of boat = 8 km/h;
Speed of stream = 3 km/h
Question 10.
Formulate the following problems as a pair of equation and then find their solution.
Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car.
Answer:
Let the speed of the train be x km/h and that of the car be y km/h
Also, we know that time =
In situation 1, time spent travelling by train = h
And time spent travelling by car = h
So, total time taken in 8hour journey is
=
⇒ …I
Again, when he travels 200km by train and rest by car
Time taken by him travel 200km by train = h
And time spent travelling by car = h
Total time taken =
But given time of journey is 8hrs 20 min i.e =
h
So, …II
Let = a and
= b
30a + 120b = 2 …III
200a + 400b = …IV
Multiply Eq. III by 20 and Eq. IV by 3
600a + 2400b = 40
600a + 1200b = 25
_- - - _
1200b = 15
b =
substitute value of b in Eq. III
30a + 120 × = 2
a =
but, ⇒ x = 60
⇒ y = 80
Speed of train = 60 km/h
Speed of car = 80 km/h
Question 11.
Formulate the following problems as a pair of equation and then find their solution.
2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.
Answer:
Let the time taken by one woman to finish the work = x days
Work done by one women in one day = days
Let the time taken by one man to finish the work = y days
Work done by one men in one day = days
Now, 2 women and 5 men can finish the work in 4 days
So, ⇒
…I
Also, 3 women and 6 men can finish the work in 3 days
So, ⇒
…II
Let be a and
be b
8a + 20b = 1 …III
9a + 18b = 1 …IV
Multiplying Eq. III by 9 and Eq. IV by 8 and solving
72a + 180b = 9
72a + 144b = 8
_- - - _
36b = 1
b =
substituting value of b in Eq. III
8a + 20 × = 1
288a + 20 = 36
288a = 16
a =
⇒ x = 18
⇒ y = 36
Number of days by man = 18;
Number of days by woman = 36