\(\left\{{}\begin{matrix}\left(2x+1\right)\left(y-2\right)=2y\left(x-3\right)\\\left(x-3\right)\left(y+1\right)=\left(x+1\right)\left(y-2\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2xy-4x+y-2=2xy-6y\\xy+x-3y-3=xy-2x+y-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-4x+y-2+6y=0\\x-3y-3+2x-y+2=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-4x+7y=2\\3x-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-12x+21y=6\\12x-16y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-12x+21y+12x-16y=6+4\\3x-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5y=10\\3x-4y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2\\3x=4y+1=4\cdot2+1=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\)
