jmc

We could solve for $x$ and $y$, then plug them in to find our answer. However, note that $(x+y{)}^2=x^2+2xy+y^2=9$ and $(x-y{)}^2=x^2-2xy+y^2=16$. Adding these two equations, we find that $(x+y{)}^2+(x-y{)}^2=2x^2+2y^2=\boxed{25}$.