\(\left\{{}\begin{matrix}5x^2y-4xy^2+3y^3-2\left(x+y\right)=0\\xy\left(x^2+y^2\right)+2=\left(x+y\right)^2\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^3+y^2x+3x^2+y^2+3x-2y+1=0\\2y^3+xy^2+y^3-3x-3=0\end{matrix}\right.\)

\(\left\{{}\begin{matrix}2x^2+x-\frac{1}{y}=2\\y-y^2x-2y^2=-2\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2+y^2=5\\x^4+y^4+6x^2y^2+20xy=81\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2+y^2+xy=3\\y^2-xy+5x+4y=9\end{matrix}\right.\)

\(\left\{{}\begin{matrix}x^2y+2x+3y=6\\3xy+x+y=5\end{matrix}\right.\)