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

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

\(\left\{{}\begin{matrix}2x^2+5xy+2y^2+x+y+1=0\\x^2+y^2+4xy+12x+12y+10=0\end{matrix}\right.\)

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