Data Sufficiency (DS) | Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0

You cannot reduce x*y = y(y + 5) by y because y can be 0 and we cannot divide by 0. By doing so you loose a root (a possible solution), namely y = 0.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
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