\(\left\{{}\begin{matrix}\dfrac{3}{2}x+2y=0\\\dfrac{x+y}{2}-\dfrac{2y}{3}=\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{2}x+2y=0\\\dfrac{x}{2}+\dfrac{y}{2}-\dfrac{2}{3}y=\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+4y=0\\\dfrac{x}{2}-\dfrac{y}{6}=\dfrac{5}{2}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}3x+4y=0\\3x-y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5y=15\\3x-y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{15}{5}=3\\3x-3=15\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3\\3x=15+3=18\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{18}{3}=6\end{matrix}\right.\)
