\(\left\{{}\begin{matrix}2x+3y=1\\x-y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}2x+3y=1\\3x-3y=9\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}5x=10\\x-y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\2-y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\y=-1\end{matrix}\right.\)