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Question
Solve for x and y:
`5/x + 6y = 13, 3/x + 4y = 7`
Solution
The given equations are:
`5/x + 6y = 13` ……..(i)
`3/x + 4y = 7 `……..(ii)
Putting` 1/x` = u, we get:
5u + 6y = 13 …….(iii)
3u + 4y = 7 ……(iv)
On multiplying (iii) by 4 and (iv) by 6, we get:
20u + 24y = 52 ……..(v)
18u + 24y = 42 ……..(vi)
On subtracting (vi) from (v), we get:
2u = 10 ⇒ u = 5
⇒ `1/x = 5 ⇒ x = 1/5`
On substituting x = 15 in (i), we get:
`5/(1⁄3) + 6y = 13`
25 + 6y = 13
6y = (13 – 25) = -12
y = -2
Hence, the required solution is x =` 1/5` and y = -2.
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