Question

Solve for x and y:

`44/(x + y) + 30/(x - y) = 10, 55/(x + y) + 40/(x - y) = 13`

Answer 1

The given equations are

`44/(x + y) + 30/(x - y) = 10`   ...(i)

`55/(x + y) + 40/(x - y) = 13`   ...(ii)

Putting `1/(x + y) = u` and `1/(x - y) = v`, we get:

44u + 30v = 10  ...(iii)

55u + 40v = 13  ...(iv)

On multiplying (iii) by 4 and (iv) by 3, we get:

176u + 120v = 40   ...(v)

165u + 120v = 39   ...(vi)

On subtracting (vi) and (v), we get:

11u = 1

⇒ `u = 1/11`

⇒ `1/(x + y) = 1/11`

⇒ x + y = 11   ...(vii)

On substituting `u = 1/11` in (iii), we get:

4 + 30v = 10

⇒ 30v = 6

⇒ `v = 6/30`

⇒ `v = 1/5`

⇒ `1/(x−y) = 1/5`

⇒ x – y = 5   ...(viii)

On adding (vii) and (viii), we get

2x = 16

⇒ x = 8

On substituting x = 8 in (vii), we get:

8 + y = 11

⇒ y = 11 – 8

⇒ y = 3

Hence, the required solution is x = 8 and y = 3.