\(\left\{{}\begin{matrix}3x-5y=17\\x+7y=-3\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}3x-5y=17\\3x+21y=-9\end{matrix}\right.\Leftrightarrow\)\(\left\{{}\begin{matrix}-26y=26\\3x+21y=-9\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-1\\3x-21=-9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=4\end{matrix}\right.\)