17.
\(\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)x+2y=1\\4x-\left(\sqrt{2}+1\right)y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)x+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\\4x-\left(\sqrt{2}+1\right)y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\\8x-2\left(\sqrt{2}+1\right)y=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}9x=\sqrt{2}+7\\x+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{\sqrt{2}+7}{9}\\\dfrac{\sqrt{2}+7}{9}+2\left(\sqrt{2}+1\right)y=\sqrt{2}+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{\sqrt{2}+7}{9}\\y=\dfrac{7-3\sqrt{2}}{9}\end{matrix}\right.\)
18.\(\left\{{}\begin{matrix}2x+y=\sqrt{2}+1\\x+y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\\sqrt{2}+y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\y=1-\sqrt{2}\end{matrix}\right.\)
19. \(\left\{{}\begin{matrix}5x-3y=4\\x+2y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}10x-6y=8\\3x+6y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=17\\x+2y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{17}{13}\\\dfrac{17}{13}+2y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{17}{13}\\y=\dfrac{11}{13}\end{matrix}\right.\)
20. \(\left\{{}\begin{matrix}-3x+2y=3\\2x+y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-3x+2y=3\\4x+2y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-7x=-7\\2x+y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\2+y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)
