ĐKXĐ: \(x;y\ne0\)
\(\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{1}{y}=1\\\dfrac{1}{x}+\dfrac{y+1}{y}=2\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{1}{y}=1\\\dfrac{1}{x}+1+\dfrac{1}{y}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{1}{y}=1\\\dfrac{1}{x}+\dfrac{1}{y}=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x}=2\\\dfrac{1}{x}+\dfrac{1}{y}=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\\dfrac{1}{2}+\dfrac{1}{y}=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\\dfrac{1}{y}=\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\y=2\end{matrix}\right.\)