Linear Equation In Two Variables Class 9th Mathematics AP Board Solution

Class 9th Mathematics AP Board Solution
Exercise 6.3
  1. 2y = -x + 1 Draw the graph of each of the following linear equations.…
  2. -x + y = 6 Draw the graph of each of the following linear equations.…
  3. 3x + 5y = 15 Draw the graph of each of the following linear equations.…
  4. x/2 - y/3 = 3 Draw the graph of each of the following linear equations.…
  5. y = x Draw the graph of each of the following linear equations.
  6. y = 2x Draw the graph of each of the following linear equations.
  7. y = -2x Draw the graph of each of the following linear equations.…
  8. y = 3x Draw the graph of each of the following linear equations.
  9. y = -3x Draw the graph of each of the following linear equations.…
  10. Answer the following question related to above graphs. i) Are all these…
  11. Draw the graph of the equation 2x + 3y = 11. Find from the graph value of y when…
  12. Draw the graph of the equation y - x = 2. Find from the graph i) the value of y…
  13. Draw the graph of the equation 2x + 3y = 12. Find the solutions from the graph…
  14. 6x - 3y = 12 Draw the graph of each of the equations given below and also find…
  15. - x + 4y = 8 Draw the graph of each of the equations given below and also find…
  16. 3x + 2y + 6 = 0 Draw the graph of each of the equations given below and also…
  17. Rajiya and Preethi two students of Class IX together collected ₹ 1000 for the…
  18. Gopaiah sowed wheat and paddy in two fields of total area 5000 square meters.…
  19. The force applied on a body of mass 6 kg. is directly proportional to the…
  20. A stone is falling from a mountain. The velocity of the stone is given by V =…
  21. In a election 60% of voters cast their votes. Form an equation and draw the…
  22. When Rupa was born, his father was 25 years old. Form an equation and draw a…
  23. An auto charges ₹ 15 for first kilometer and ₹ 8 each for each subsequent…
  24. A lending library has fixed charge for the first three days and an additional…
  25. The parking charges of a car in Hyderabad Railway station for first two hours…
  26. Sameera was driving a car with uniform speed of 60 kmph. Draw distance-time…
  27. The ratio of molecular weight of Hydrogen and Oxygen in water is 1:8. Set up an…
  28. In a mixture of 28 litres, the ratio of milk and water is 5:2. Set up the…
  29. In countries like USA and Canada temperature is measured in Fahrenheit where as…
Exercise 6.4
  1. a) On the number line and b) On the Cartesian plane x = 3 Give the graphical…
  2. a) On the number line and b) On the Cartesian plane y + 3 = 0 Give the…
  3. a) On the number line and b) On the Cartesian plane y = 4 Give the graphical…
  4. a) On the number line and b) On the Cartesian plane 2x - 9 = 0 Give the…
  5. a) On the number line and b) On the Cartesian plane 3x + 5 = 0 Give the…
  6. Give the graphical representation of 2x - 11 = 0 as an equation in i) one…
  7. Solve the equation 3x + 2 = 8x - 8 and represent the solution on i) the number…
  8. Write the equation of the line parallel to X-axis, and passing through the point…
  9. Write the equation of the line parallel to Y-axis and passing through the point…
  10. Write the equation of three lines that are (i) parallel to the X-axis (ii)…

Exercise 6.3
Question 1.

Draw the graph of each of the following linear equations.

2y = -x + 1


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 2.

Draw the graph of each of the following linear equations.

–x + y = 6


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 3.

Draw the graph of each of the following linear equations.

3x + 5y = 15


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 4.

Draw the graph of each of the following linear equations.



Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 5.

Draw the graph of each of the following linear equations.

y = x


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 6.

Draw the graph of each of the following linear equations.

y = 2x


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 7.

Draw the graph of each of the following linear equations.

y = -2x


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 8.

Draw the graph of each of the following linear equations.

y = 3x


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:




Question 9.

Draw the graph of each of the following linear equations.

y = -3x


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.) Table of solutions for the given equation-



GRAPH:




Question 10.

Answer the following question related to above graphs.

i) Are all these equations of the form y = mx, where m is a real number?

ii) Are all these graphs passing through the origin?

iii) What can you conclude about these graphs?


Answer:

(i) Yes, all these are equations of the form y = mx, where m is a real number and m = 1,2,-2,3,-3 respectively in the above equations.


(ii) Yes, all these are graphs passing through the origin, i.e., pt. A in every graph


(iii) ∴ we can conclude that every graph of type y = mx passes through origin, where m is a real number.



Question 11.

Draw the graph of the equation 2x + 3y = 11. Find from the graph value of y when x = 1


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:



From the graph (pt. E) we can see that for x = 1, the y = 3.


(Note: Also we can put x = 1 in the given equation and can find the value of y-


We have,


At x = 1,



⇒ y = 3



Question 12.

Draw the graph of the equation y - x = 2. Find from the graph

i) the value of y when x = 4

ii) the value of x when y = -3


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:



i)the value of y when x = 4 is y = 6 (pt. E)


ii) the value of x when y = -3 is y = -5 (pt. F)



Question 13.

Draw the graph of the equation 2x + 3y = 12. Find the solutions from the graph

i) Whose y-coordinate is 3

ii) Whose x-coordinate is -3


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.

(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:



(i) From the graph, we can see that for y = 3 is pt. E and the



(ii) From the graph, we can see that for x = -3 is pt. F and the corresponding y = 6 for that.



Question 14.

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

6x - 3y = 12


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.


(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:



⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (2,0) and pt. B = (0,-4)



Question 15.

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

- x + 4y = 8


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.


(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-




⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (-8,0) and pt. B = (0,2).



Question 16.

Draw the graph of each of the equations given below and also find the coordinates of the points where the graph cuts the coordinate axes

3x + 2y + 6 = 0


Answer:

For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.


(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH:



⇒ ∴ the pts. Where graph cuts the co-ordinate axis(i.e., where x = 0 and where y = 0) are pt. A = (-2,0) and pt. B = (0,-3).



Question 17.

Rajiya and Preethi two students of Class IX together collected ₹ 1000 for the Prime Minister Relief Fund for victims of natural calamities. Write a linear equation and draw a graph to depict the statement.


Answer:

Given that together Rajiya and Preethi collected Rs.1000.

Now, Let the amount collected by Rajiya be Rs. x and by Preethi be Rs. y.


∴ the linear equation will be-


⇒ x + y = 1000


For graph, we’ll first make the table of solutions by putting some random values of x and thereafter we’ll find corresponding values of y and then we’ll plot these points on graph, join them and extend them in straight line to find the graph.


(Note: ∵ equation is linear graph will always be straight line.)


Table of solutions for the given equation-



GRAPH: