ĐKXĐ: \(y\ne0\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy+x+y=3\\xy\left(x+y\right)=2\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}x+y=u\\xy=v\end{matrix}\right.\) với \(u^2\ge4v\)
\(\Rightarrow\left\{{}\begin{matrix}u+v=3\\uv=2\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}u=1\\v=2\end{matrix}\right.\) (loại) hoặc \(\left\{{}\begin{matrix}u=2\\v=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+y=2\\xy=1\end{matrix}\right.\) \(\Rightarrow x=y=1\)
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