Q1 of 40 Page 98

Solve each of the following pairs of equations by reducing them to a pair of linear equation.


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


More from this chapter

All 40 →
1

Solve each of the following pairs of equations by reducing them to a pair of linear equation.


 1

Solve each of the following pairs of equations by reducing them to a pair of linear equation.


 2

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.

 2

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.