\(\left\{{}\begin{matrix}\dfrac{3}{x+1}+\dfrac{6}{y}=4\\\dfrac{2}{x+1}-\dfrac{1}{y}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x+1}+\dfrac{6}{y}=4\\\dfrac{-12}{x+1}+\dfrac{6}{y}=-6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x+1}+\dfrac{6}{y}-\left(\dfrac{-12}{x+1}+\dfrac{6}{y}\right)=4-\left(-6\right)\\\dfrac{3}{x+1}+\dfrac{6}{y}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{15}{x+1}=10\\\dfrac{3}{x+1}+\dfrac{6}{y}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}15=10\left(x+1\right)\\\dfrac{3}{x+1}+\dfrac{6}{y}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\\dfrac{3}{2+1}+\dfrac{6}{y}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\1+\dfrac{6}{y}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\\dfrac{6}{y}=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=2\end{matrix}\right.\)
