jmc

Adding all four equations together results in $3w+3x+3y+3z=33\Rightarrow w+x+y+z=11$. Subtracting the four original equations from this sum gives: $z=11-(-2)=13$, $y=11-4=7$, $x=11-19=-8$, and $w=11-12=-1$, respectively. Therefore, $wx+yz=-1\cdot -8+7\cdot 13=8+91=\boxed{99}$