\(\left\{{}\begin{matrix}x+2y=m+3\\2x-3y=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x+2y=2x-3y+3\\2x-3y=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5y-x=3\\2x-3y=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5y-3=x\\2\left(5y-3\right)-3y=m\end{matrix}\right.\\\Leftrightarrow\left\{{}\begin{matrix}5y-3=x\\10y-6-3y=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5y-3=x\\7y-6=m\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}5.\dfrac{m+6}{7}-3=x\\y=\dfrac{m+6}{7}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5m+30}{7}-3=x\\y=\dfrac{m+6}{7}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5m+21}{7}\\y=\dfrac{m+6}{7}\end{matrix}\right.\)
\(x+y=-3\\ \Leftrightarrow\dfrac{5m+21}{7}+\dfrac{m+6}{7}=-3\\ \Leftrightarrow\dfrac{5m+21+m+6}{7}=-3\\ \Leftrightarrow6m+27=-21\\ \Leftrightarrow6m=-48\\ \Leftrightarrow m=-8\)
