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Question
Solve for x and y:
`x + 6/y = 6, 3x - 8/y = 5`
Solution
The given equations are:
x + `6/y` = 6 ……..(i)
3x - `8/y` = 5 ……..(ii)
Putting `1/y` = v, we get:
x + 6v = 6 …….(iii)
3x – 8v = 5 ……(iv)
On multiplying (iii) by 4 and (iv) by 3, we get:
4x + 24v = 24 ……..(v)
9x – 24v = 15 ……..(vi)
On adding (v) from (vi), we get:
13x = 39 ⇒ x = 3
On substituting x = 3 in (i), we get:
3 + `6/y` = 6
⇒`6/y` = (6 – 3) = 3 ⇒ 3y = 6 ⇒ y = 2
Hence, the required solution is x = 3 and y = 2.
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