Question

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

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)x+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\\8x-2\left(\sqrt{2}+1\right)y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\\8x-2\left(\sqrt{2}+1\right)y=6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}9x=\sqrt{2}+7\\y=\dfrac{1-\left(\sqrt{2}-1\right)x}{2}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{7+\sqrt{2}}{9}\\y=\dfrac{7-3\sqrt{2}}{9}\end{matrix}\right.\)