If $x$ and $y$ are non-zero integers and $|x| + |y| = 32,$ what is $xy?$

If $x$ and $y$ are non-zero integers and $|x| + |y| = 32,$ what is $xy?$

(1) $-4x - 12y = 0$

(2) $|x| - |y| = 16$

Answer: A

Source: Manhattan GMAT

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