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Question
Solve for x and y:
`9/x - 4/y = 8, (13)/x + 7/y = 101`
Solution
The given equations are:
`9/x - 4/y = 8` ……..(i)
`(13)/x + 7/y = 101` ……..(ii)
Putting `1/x= u and 1/y`= v, we get:
9u - 4v = 8 …….(iii)
13u + 7v = 101 ……(iv)
On multiplying (iii) by 7 and (iv) by 4, we get:
63u - 28v = 56 ……..(v)
52u + 28v = 404 ……..(vi)
On adding (v) from (vi), we get:
115u = 460 ⇒ u = 4
⇒`1/x = 4 ⇒ x = 1/4`
On substituting x =`1/4` in (i), we get:
`9/(1⁄4) - 4/y = 8`
⇒`36 - 4/y = 8 ⇒ 4/y= (36 – 8) = 28`
y = `4/28 = 1/7`
Hence, the required solution is x = `1/4 and y = 1/7`.
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