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Question
Solve for x and y:
`3/x - 1/y + 9 = 0, 2/x + 3/y = 5`
Solution
`3/x - 1/y + 9 = 0,`
`⇒3/x - 1/y = -9 ……..(i)`
`⇒2/x - 3/y = 5……..(ii)`
Putting `1/x = u and 1/y = v, we get:`
3u – v = -9 …….(iii)
2u + 3v = 5 ……(iv)
On multiplying (iii) by 3, we get:
9u – 3v = -27 ……..(v)
On adding (iv) and (v), we get:
11u = -22 ⇒ u = -2
`⇒1/x = -2 ⇒ x = (−1)/2`
On substituting x = `(−1)/2` in (i), we get:
`3/(−1⁄2) - 1/y = -9`
`⇒-6 - 1/y= -9 ⇒ 1/y = ( -6 + 9) = 3`
`⇒y = 1/3`
Hence, the required solution is x =`( −1)/2 and y = 1/3`
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