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 .
