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

⇒ y = 2

Hence, x = 3 and y = 2.