(ans. $4:(2,0),(0,2),(-2,0),(0,-2)$.
The cases are (A) $|x y|=0$ and $|x-y|=2 \Rightarrow(x, y)=(0, \pm 2),( \pm 2,0)$; (B) $|x y|=2$ and $|x-y|=0 \Rightarrow$ no solution; (C) $|x y|=|x-y|=1 \Rightarrow$ no solution.)
9. How many pairs of integers solve the system $|x y|+|x-y|=2$ if $-10 \leq x, y \leq 10 ?$