ĐKXĐ:\(\left\{{}\begin{matrix}x\ne-1\\y\ne-1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{y}{y+1}=2\\\dfrac{x}{x+1}+\dfrac{3y}{y+1}=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{y}{y+1}=2\\\dfrac{2x}{x+1}+\dfrac{6y}{y+1}=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{y}{y+1}=2\\\dfrac{2x}{x+1}+\dfrac{6y}{y+1}-\dfrac{2x}{x+1}-\dfrac{y}{y+1}=2-\left(-2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{y}{y+1}=2\\\dfrac{5y}{y+1}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{4}{4+1}=2\\y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{6x}{x+1}+\dfrac{3y}{y+1}=2\\\dfrac{x}{x+1}+\dfrac{3y}{y+1}=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5x}{x+1}=3\\\dfrac{6x}{x+1}+\dfrac{3y}{y+1}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\\dfrac{18}{5}+\dfrac{3y}{y+1}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\\dfrac{3y}{y+1}=-\dfrac{8}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\3y=-\dfrac{8}{5}y-\dfrac{8}{5}\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}x=\dfrac{3}{2}\\\dfrac{23}{5}y=-\dfrac{8}{5}\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-\dfrac{8}{23}\end{matrix}\right.\)
