In two dimensions we can reduce the static equilibrium equations. Because the $z$ axis will experience no [[Force|forces]] in two dimensions we can omit the $F_z$ term. The only [[Moment|moment]] present in a 2D system is $M_z$, since it is the only possible moment that can be made using $F_x$ and $F_y$.
$\sum F_x=0$
$\sum F_y=0$
$\sum M_z=0$