$\left\{\begin{matrix}x^{2}+xy+2=3x+y & &\\x^{2}+y^{2}=2 & &\end{matrix}\right.$
$\left\{\begin{matrix}x^{2}+xy+x+y=4 & & \\ \left ( x+y \right )+\left ( 1+xy \right )=4 &&\end{matrix}\right.$
$\left\{\begin{matrix}xy\left ( x+y \right ) =2 & & \\ x^{3}+y^{3}+x+y=4 & & \end{matrix}\right.$