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Question
Solve for x and y:
`5/x - 3/y = 1, 3/(2x )+ 2/(3y) = 5`
Solution
The given equations are:
`5/x - 3/y = 1` ……..(i)
`3/(2x )+ 2/(3y) = 5` ……..(ii)
Putting` 1/x = u and 1/y`= v, we get:
5u - 3v = 1 …….(iii)
⇒`3/2 u + 2/3 v = 5`
⇒`(9u+4v)/6 = 5`
⇒9u + 4v = 30 …….(iv)
On multiplying (iii) by 4 and (iv) by 3, we get:
20u - 12v = 4 ……..(v)
27u + 12v = 90 ……..(vi)
On adding (iv) and (v), we get:
47u = 94 ⇒ u = 2
⇒`1/x = 2 ⇒ x = 1/2`
On substituting x = 12 in (i), we get:
`5/(1⁄2) - 3/y = 1`
`⇒10 - 3/y = 1 ⇒ 3/y= (10 – 1) = 9`
`y = 3/9 = 1/3`
Hence, the required solution is x = `1/2 and y = 1/3`.
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