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