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Question
Solve the following pairs of equations:
`(x + y)/(xy)` = 2
`(x - y)/(xy)` = 6
Solution
`(x + y)/(xy)` = 2
⇒ x + y = 2xy ....(i)
`(x - y)/(xy)` = 6
⇒ x - y = 6xy ....(ii)
Adding eqns. (i) and (ii), we get
2x = 8xy
⇒ y = `(1)/(4)`
Substituting the value of y in eqn. (i), we get
`x + (1)/(4) = 2x xx (1)/(4)`
⇒ `(4x + 1)/(4) = x/(2)`
⇒ 8x + 2 = 4x
⇒ 4x = -2
⇒ x = `-(1)/(2)`
Thus, the solution set is `(-1/2, 1/4)`.
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