\(\left\{{}\begin{matrix}x+2y-3=0\\x\left(y+2\right)+y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2y+3\\-2y+3\left(y+2\right)+y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2y+3\\2y+6=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=0\end{matrix}\right.\)