The Number Of Pairs (x, y) Satisfying The Equations

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Question

The number of pairs (x, y) satisfying the equations

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Solution

Correct option is

The first equation can be written as

When x + y = 0, we have to reject x + y = 1 or –1 and solve it with x – y = 1 or x – y = –1 which give (1/2, –1/2) or (–1/2, 1/2) as the possible solutions. Again solving with x = 0 we get and solving with y = 0 we get as the other solutions. Thus we have six sets of solutions for x and y.