$\left\{\begin{matrix} x^{2}+2x+y^{2}+y=3-xy & & \\ xy+x+2y=1 & & \end{matrix}\right.$
$\left\{\begin{matrix} 5x^{2}y-4xy^{2}+3y^{3}-2(x+y)=0 & & \\ xy(x^{2}+y^{2})+2=(x+y)^{2} & & \end{matrix}\right.$
$\left\{\begin{matrix} xy^{2}+6x^{2}=-y & & \\ x^{3}y^{3}-19x^{3}=-1 & & \end{matrix}\right.$
$\left\{\begin{matrix} -x+7y-xy=1 & & \\ x^{2}y^{2}+xy-13y^{2}=-1 & & \end{matrix}\right.$