Question

Find the solution of the pair of equations `x/10 + y/5 - 1` = 0 and `x/8 + y/6` = 15. Hence, find λ, if y = λx + 5.

Answer 1

Given pair of equations is

`x/10 + y/5 - 1` = 0

⇒ x + 2y – 10 = 0  ......(i)

⇒ x + 2y = 10   

And `x/8 + y/6` = 15

⇒ 3x + 4y = 360   ......(ii)

On multiplying equation (i) by 2 and then subtracting from equation (ii), we get

(3x + 4y) – (2x + 4y) = 360 – 20

⇒ x = 340

Put the value of x in equation (i), we get

340 + 2y = 10

⇒ 2y = 10 – 340 = –330

⇒ y = –165

Now, y = λx + 5

Put the values of x and y in above relation, we get

–165 = λ(340) + 5

⇒ 340λ = –170

⇒ λ = `- 1/2`

Hence, the solution of the pair of equations are x = 340, y = –165 and the required value of λ is `- 1/2`.