If $x=y$, $x=y=0$, $\pm \sqrt{5}$. If $x=-y$, $x=-y=\pm \sqrt{7}$. Otherwise, $x^2+xy+y^2=7$ and $x^2-xy+y^2=5$. Thus, $xy=1$ and $x^2+y^2=6$. $x+y=\pm 2\sqrt{2}$ and $x-y=\pm 2$, so $x= \pm \sqrt{2} \pm 1$ and $y=\pm \sqrt{2} \mp 1$.