\(\left\{{}\begin{matrix}2x+3y=1\\3x-2y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=1-3y\\3x-2y=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{3}{2}y\\3\left(\dfrac{1}{2}-\dfrac{3}{2}y\right)-2y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{3}{2}y\\\dfrac{3}{2}-\dfrac{9}{2}y-2y=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{3}{2}y\\\dfrac{3}{2}-\dfrac{13}{2}y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}-\dfrac{3}{2}y\\\dfrac{13}{2}y=\dfrac{3}{2}+5=\dfrac{13}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=1\\x=\dfrac{1}{2}-\dfrac{3}{2}\cdot1=\dfrac{1}{2}-\dfrac{3}{2}=-\dfrac{2}{2}=-1\end{matrix}\right.\)
