\(\left\{{}\begin{matrix}3x-y\sqrt{2}=1\\x+2y\sqrt{2}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2y\sqrt{2}=2\\x+2y\sqrt{2}=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x-2y\sqrt{2}+x+2y\sqrt{2}=2+5\\3x-y\sqrt{2}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}7x=7\\y\sqrt{2}=3y-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y\sqrt{2}=3-1=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=1\\y=\sqrt{2}\end{matrix}\right.\)
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