Question

\(\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)x-y=\sqrt{2}\\x+\left(\sqrt{2}+1\right)y=1\end{matrix}\right.\)

Answer 1

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

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

\(\Rightarrow2x=3+\sqrt{2}\Rightarrow x=\frac{3+\sqrt{2}}{2}\)

\(\Rightarrow y=\frac{1-x}{\sqrt{2}+1}=-\frac{1}{2}\)