\(\left\{{}\begin{matrix}\dfrac{x-1}{3}+\dfrac{y}{2}=1\\\dfrac{x+3}{2}-\dfrac{y-1}{3}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{2x-2+3y}{6}=1\\\dfrac{3\left(x+3\right)-2\left(y-1\right)}{6}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+3y-2=6\\3x+9-2y+2=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+3y=8\\3x-2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+9y=24\\6x-4y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}13y=22\\3x-2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{22}{13}\\3x=1+2y=1+\dfrac{44}{13}=\dfrac{57}{13}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{22}{13}\\x=\dfrac{19}{13}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+3y=8\\3x-2y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\y=\dfrac{22}{13}\end{matrix}\right.\)
