Question

Solve for x and y:
`3/(x+y) + 2/(x−y)= 2, 3/(x+y) + 2/(x−y) = 2`

Answer 1

The given equations are
`3/(x+y) + 2/(x−y) = 2 `    ……(i)
`9/(x+y) - 4/(x−y) = 1`    ……(ii)
Substituting`1/(x+ y) = u and 1/(x−y)` = v, we get:
3u + 2v = 2 ……..(iii)
9u - 4v = 1 …….(iv)
On multiplying (iii) by 2, we get:
6u + 4v = 4 …..(v)
On adding (iv) and (v), we get:
15u = 5
`⇒u = 5/15 = 1/3`
`⇒ 1/(x+y) = 1/3 ⇒ x + y =3`    …….(vi)
On substituting u = `1/3` in (iii), we get
1 + 2v = 2
⇒2v = 1
⇒`v = 1/2`
⇒ `1/(x−y) = 1/2 ⇒ x – y = 2`    …….(vii)
On adding (vi) and (vii), we get
2x = 5

⇒ x = `5/2`
On substituting x = `5/2` in (vi), we have
`5/2 + y = 3`
`⇒ y = (3 – 5/2) = 1/2`
Hence, the required solution is x = `5/2 and y = 1/2`.