\(\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1\\\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\end{matrix}\right.\) (2x \(\ne\) y; x \(\ne\) -y)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}\dfrac{3}{2x-y}-\dfrac{6}{x+y}=-1\\\dfrac{3}{2x-y}-\dfrac{3}{x+y}=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}\dfrac{-3}{x+y}=-1\\\dfrac{1}{2x-y}-\dfrac{1}{x+y}=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x+y=3\\\dfrac{1}{2x-y}-\dfrac{1}{3}=0\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x+y=3\\2x-y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}3x=6\\x+y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\2+y=3\end{matrix}\right.\)
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\) (TM)
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