\(\left\{{}\begin{matrix}x^2-\dfrac{1}{y-1}=2\\2x^2+\dfrac{3}{1-y}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+\dfrac{1}{1-y}=2\\2x^2+\dfrac{1}{1-y}+\dfrac{2}{1-y}=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+\dfrac{1}{1-y}=2\\x^2+\dfrac{2}{1-y}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+\dfrac{1}{1-y}=2\\\dfrac{1}{1-y}=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2=2-\dfrac{1}{1-y}\\1-y=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2=2-\dfrac{1}{1-y}=2-\dfrac{1}{1-\dfrac{3}{2}}=4\\y=1+\dfrac{1}{2}=\dfrac{3}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\mp2\\y=\dfrac{3}{2}\end{matrix}\right.\)