Question

Solve the following simultaneous equations.

`2/(x + y) - 3/(x - y)` = 15; `8/(x + y) + 5/(x - y)` = 77

Answer 1

`2/(x + y) - 3/(x - y)` = 15   ...(i)

`8/(x + y) + 5/(x - y)` = 77   ...(ii)

`u = 1/(x+y), v = 1/(x-y)` 

2u − 3v = 15   ...(iii)

8u + 5v = 77   ...(iv)

Multiply (3) by 5 and (4) by 3 to eliminate v:

10u − 15v = 75   ...(v)

24u + 15v = 231   ...(vi)

34u = 306 ⇒ u = `306/34 = 9`

2(9) − 3v = 15 ⇒ 18 − 3v = 15 ⇒ v = 1

`1/(x+y) = 9 => x+y=1/9`

`1/(x-y) = 1 => x - y = 1`

`(x+y)+(x-y) = 1/9+1 => 2x = 10/9 => x = 5/9`

`x+y=1/9 => 5/9+y=1/9 => y=-4/9`

`x=5/9, y=-4/9`