3. The number of integer solutions to the equation $|x y|+|x+y|=1$ is ( ).
(A) 2
(B) 4
(C) 6
(D) 8
3.C.

Since $x, y$ are integers, then $|xy|, |x+y|$ are non-negative integers. Therefore, one of $|xy|, |x+y|$ is 0, and the other is 1. Considering the cases, we get 6 solutions.