\(\left\{{}\begin{matrix}\frac{3}{x-2}+\frac{2}{y+1}=\frac{17}{5}\\\frac{2x-2}{x-2}+\frac{y+2}{y+1}=\frac{26}{5}\end{matrix}\right.\)

\(\left\{{}\begin{matrix}\frac{2x+1}{4}-\frac{y-2}{3}=\frac{1}{12}\\\frac{x+5}{2}=\frac{y+7}{3}-4\end{matrix}\right.\)

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

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

\(\left\{{}\begin{matrix}\frac{1-x+2y}{x-2y}+x+2y=4\\\frac{x+2y}{x-2y}-6=0\end{matrix}\right.\)

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

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

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

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

\(\left\{{}\begin{matrix}x-2\sqrt{2}y=\sqrt{5}\\\sqrt{2}+y=1-\sqrt{10}\end{matrix}\right.\)