Solve : ` (3)/(x + y ) + ( 2)/(x - y ) = 2 and (9)/(x + y ) - ( 4)/(x - y) = 1 `.

Options

A. ` x = (1)/(2), y = (3)/(2)`
B. `x = (5)/(2), y = (1)/(2) `
C. ` x = (3)/(2), y = (1)/(2)`
D. ` x = (1)/(2), y = (5)/(2)`.

Answer

B

Explanation

Put ` (1)/(x + y ) = u and (1)/(x - y ) =v ` to get ` 3u + 2 v = 2 and 9u - 4v = 1 `.
Solve for u and v to get ` u = (1)/(3) and v = (1)/(2)`.
` therefore x + y = 3 and x - y = 2`.