\(\left\{{}\begin{matrix}4x+y=-5\\3x+12=2y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x+y=-5\\3x-2y=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-4x-5\\3x-2\left(-4x-5\right)=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-4x-5\\3x+8x+10=-12\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-4x-5\\11x=-22\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-4x-5\\x=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=3\end{matrix}\right.\)