\(\left\{{}\begin{matrix}x\left(\sqrt{3}+1\right)+y=2\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)+y\left(\sqrt{3}-1\right)=2\left(\sqrt{3}-1\right)\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y\left(\sqrt{3}-1\right)=2\sqrt{3}-2\\2x-y\left(\sqrt{3}-1\right)=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y\left(\sqrt{3}-1\right)+2x-y\left(\sqrt{3}-1\right)=2\sqrt{3}-2+6-2\sqrt{3}\\\left(\sqrt{3}+1\right)x+y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x=4\\y=2-x\left(\sqrt{3}+1\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2-\sqrt{3}-1=1-\sqrt{3}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\left(1+\sqrt{3}\right)x+y=2\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)x+\left(\sqrt{3}-1\right)y=2\left(\sqrt{3}-1\right)\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2x+\left(\sqrt{3}-1\right)y=2\sqrt{3}-2\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left(1+\sqrt{3}\right)x+y=2\\4x=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}1+\sqrt{3}+y=2\\x=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1-\sqrt{3}\\x=1\end{matrix}\right.\)
