Question

Solve for x and y:
`5/(x+y) - 2/(x−y) = -1, 15/(x+y) - 7/(x−y) = 10`

Answer 1

The given equations are
`5/(x+y) - 2/(x−y)= -1`   ……(i)
`15/(x+y) - 7/(x−y) = 10`   ……(ii)
Substituting `1/(x+y) = u and 1/(x−y) = v` in (i) and (ii), we get
5u – 2v = -1 ……..(iii)
15u + 7v = 10 …….(iv)
Multiplying (iii) by 3 and subtracting it from (iv), we get
7v + 6v = 10 + 3
⇒13v = 13
⇒v = 1

`⇒x – y = 1 (∵1/(x−y)=v)`     …..(v)
Now, substituting v = 1 in (iii), we get
5u – 2 = -1
⇒5u = 1
`⇒u = 1/5`
x + y = 5            …….(vi)
Adding (v) and (vi), we get
2x = 6 ⇒ x = 3
Substituting x = 3 in (vi), we have
3 + y = 5 ⇒ y = 5 – 3 = 2
Hence, x = 3 and y = 2.