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Question
Solve the following pairs of equations:
`(xy)/(x + y) = (6)/(5)`
`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0
Solution
`(xy)/(x + y) = (6)/(5)`
⇒ `(x + y)/(xy) = (5)/(6)`
⇒ `(1)/y + (1)/x = (5)/(6)` ....(i)
`(xy)/(y - x)` = 6
⇒ `(y - x)/(xy)` = 6
⇒ `(1)/x + (1)/y = (1)/(6)` ....(ii)
Adding eqns. (i) and (ii), we get
`(2)/x` = 1
⇒ x = 2
⇒ `(1)/y + (1)/(2) = (5)/(6)`
⇒ `(1)/y = (5)/(6) - (1)/(2)`
= `(5 - 3)/(6)`
= `(2)/(6)`
= `(1)/(3)`
⇒ y = 3
Thus, the solution set is (2, 3).
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