Question

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

`10/(x+y) + 2/(x-y) = 4`

`15/(x+y) - 5/(x-y) = -2`

Answer 1

`10/(x+y) + 2/(x-y) = 4`

`15/(x+y) - 5/(x-y) = -2`

Putting  `1/x+y = p ` in the given equations, we get:

10p + 2q = 4

⇒ 10p + 2q - 4 = 0 ... (i)

15p - 5q = -2

⇒ 15p - 5q + 2 = 0 ... (ii)

Using cross multiplication, we get

`p/(4-20) = q/(-60-(-20)) = 1/(-50-30)`

`p/-16 = q/-80 = 1/-80`

`p/-16 = 1/-80 `

p = 1/5 and q = 1

`p = 1/(x+y) = 1/5 and q = 1/(x-y) = 1`

x + y = 5 ... (iii)

and x - y = 1 ... (iv)

Adding equation (iii) and (iv), we get

2x = 6

x = 3 .... (v)

Putting value of x in equation (iii), we get

y = 2

Hence, x = 3 and y = 2