GIVEN :(x+y) = (a-z) Transform the 2nd equation into
(x+y)/xy + 1/z = 1/a. Substitute for (x+y) and simplify into az(a-z) + xy(a-z) = 0
i.e. ( a-z)(az+xy)= 0 with z=a being a candidate answer.

By symmetry we could get x=a or y=a in the same way.

QED

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