Practice Set 1.4 Linear Equations In Two Variables Class 10th Mathematics Part 1 MHB Solution

Practice Set 1.4

2/x - 3/y = 15 8/x + 5/y = 77 Solve the following simultaneous equation.…

10/x+y + 2/x-y = 4 15/x+y - 5/x-y = - 2 Solve the following simultaneous equation.…

27/x-2 + 31/y+3 = 85 31/x-2 + 27/y+3 = 89 Solve the following simultaneous equation.…

1/3x+y + 1/3x-y = 3/4 1/2 (3x+y) - 1/2 (3x-y) = 1/8 Solve the following simultaneous…

Practice Set 1.4

Question 1.

Solve the following simultaneous equation.

Answer:

Let  = m and = n

Multiply Eq. I by 4

Equating Eq. II and III. Change the signs of Eq. III

Substituting n=1 in Eq. II

∴  ⇒  ⇒ 

∴  ⇒  ⇒ 

Hence (x,y) = (

Question 2.

Solve the following simultaneous equation.

Answer:

Let  = m and = n

Multiply Eq. I by 5 and Eq.II by 2

Substituting  in Eq. I

∴  ⇒  ⇒  ….(III)

∴  ⇒  ⇒ ….(IV)

Now, equating Eq. III and IV

Subsituting value of x=3 in Eq. III

Hence (x,y) = (

Question 3.

Solve the following simultaneous equation.

Answer:

Let  = m and = n

Adding both equations

Dividing both sides by 58

 …(III)

Subtracting Eq. I and II

Dividing both sides by 4

 …(IV)

Equating Eq. III and IV

Subsituting n=1 in Eq. III

∴  ⇒  ⇒  ⇒  ⇒ 

⇒  ⇒ 

∴  ⇒  ⇒ ⇒  ⇒ 

Hence (x,y) = (

Question 4.

Solve the following simultaneous equation.

Answer:

Let  = m and = n

⇒ 

 ⇒ 

Multiply Eq. I by 2

 .... (a)

 ..... (b)

Add (a) and (b) to get,


8m + 8n + 8m - 8n = 8

⇒ 16m = 8

Substituting  in Eq. II

⇒ 4 - 8n = 2

⇒ - 8n = 2 - 4

⇒ - 8n = -2

⇒ 8n = 2

⇒ 

⇒

∴ 

⇒ 

⇒ 2 = 2 (3x+y)

⇒ 2 = 6x + 2y ...... III

∴ 

⇒ 

⇒ 4 = 2(3x - y)

⇒ 4 = 6x - 2y ….IV

Add Eq. III and IV

Substituting 

⇒ 3 + 2y = 2

⇒ 2y = 2 - 3

⇒ 2y = -1

Hence (x,y) = (