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

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

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

\(\frac{x^2+x+1}{x^2+2x+1}+\frac{x^2+3x+1}{x^2+4x+1}=\frac{19}{12}\)