\(\left\{{}\begin{matrix}\frac{2x+3y-1}{x-y+2}=\frac{12}{13}\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{2x+3y+2-3}{x-y+2}=\frac{12}{13}\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{-3}{x-y+2}=\frac{12}{13}\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-4\left(x-y+2\right)=13\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-4x+4y-8=13\\4x+6y+4=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-4x+4y-8+4x+6y+4=13\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}10y=17\\2x+3y+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=1,7\\x=-3,55\end{matrix}\right.\)
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