Question

Find the solution of the pair of the equation :
`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0

Answer 1

The given equations are

`3/x + 8/y = - 1`         ...(1)
`1/x - 2/y = 2`            ...(2)

Let `1/x = u and 1/y = v`
(1) and (2) will become
3u + 8v = -1           ...(3)
u - 2v = 2               ...(4)

Multiply (4) with 4
4u - 8v = 8            ...(5)
Adding (3) and (5) we get
7u = 7
⇒ u = 1

Putting this value in (4)
1 - 2v = 2
⇒ v = `(-1)/2`

Now
`1/x = u`
⇒ `1/x = 1`
⇒  x = 1

And
`1/y = v`
⇒ `1/y = (-1)/2`
⇒ y = - 2