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Solve the simultaneous equations: (x + y)/(x - y) + (x - y)/(x + y) = 13/6 and x*y = 5.

1. (x, y) = (5, 1) or (1, 5) or (-5, -1) or (-1, -5)
2. (x, y) = (5, 1) or (1, 5) only
3. (x, y) = (2.5, 2) or (2, 2.5)
4. No real solution

Correct answer: (x, y) = (5, 1) or (1, 5) or (-5, -1) or (-1, -5)

Solution

Setting t = (x+y)/(x-y) turns equation one into a solvable quadratic. Each value of t gives a linear ratio between x and y, which with xy = 5 yields the pairs.

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