\(\left\{{}\begin{matrix}x\cdot\sqrt{2}-3y=11\\\left(1-\sqrt{2}\right)x+\left(1+\sqrt{2}\right)y=-4\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{2}\left(1-\sqrt{2}\right)x-3y\cdot\left(1-\sqrt{2}\right)=11\left(1-\sqrt{2}\right)\\\sqrt{2}\left(1-\sqrt{2}\right)x+\sqrt{2}\left(1+\sqrt{2}\right)y=-8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y\left(-3+3\sqrt{2}-\sqrt{2}-2\right)=11-11\sqrt{2}+8=19-11\sqrt{2}\\x\sqrt{2}-3y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-3+\sqrt{2}\\x\sqrt{2}=2+3\sqrt{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3+\sqrt{2}\\y=-3+\sqrt{2}\end{matrix}\right.\)
