Question

Solve the following systems of 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`

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

The given equations reduce to:

10p + 2q = 4

=> 10p + 2q - 4 = 0 ....(1)

15p - 5q = -2 

=> 15p - 5q + 2 = 0 ...(2)

Using cross-multiplication method, we obtain:

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

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

p = 1/5 and q =1

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

x + y = 5 .....(3)

x - y = 1 ....(4)

Adding equation (3) and (4), we obtain:

2x = 6

x = 3

Substituting the value of x in equation (3), we obtain:

y = 2

∴ x = 3, y = 2