a: \(\left\{{}\begin{matrix}2x+y=8\\2x-3y=-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+y-2x+3y=8+4\\2x+y=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4y=12\\2x=8-y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\2x=8-3=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=3\\x=\dfrac{5}{2}\end{matrix}\right.\)
b:
\(\left\{{}\begin{matrix}x\sqrt{2}-y=3\sqrt{2}\\x+\sqrt{2}y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y\sqrt{2}=6\\x+\sqrt{2}y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-y\sqrt{2}+x+\sqrt{2}y=6+3\\x\sqrt{2}-y=3\sqrt{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x=9\\y=x\sqrt{2}-3\sqrt{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=0\end{matrix}\right.\)
c:
\(\left\{{}\begin{matrix}0,3x+0,2y=0,5\\0,2x-0,5y=2,5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+2y=5\\2x-5y=25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}15x+10y=25\\4x-10y=50\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}15x+10y+4x-10y=25+50\\2x-5y=25\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}19x=75\\5y=2x-25\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{75}{19}\\y=\dfrac{2x-25}{5}=\dfrac{2\cdot\dfrac{75}{19}-25}{5}=-\dfrac{65}{19}\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}x\left(1+\sqrt{3}\right)+y=2\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)+y\left(\sqrt{3}-1\right)=2\left(\sqrt{3}-1\right)\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y\left(\sqrt{3}-1\right)=2\sqrt{3}-2\\2x-\left(\sqrt{3}-1\right)y=6-2\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y\left(\sqrt{3}-1\right)+2x-y\left(\sqrt{3}-1\right)=2\sqrt{3}-2+6-2\sqrt{3}\\x\left(1+\sqrt{3}\right)+y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x=4\\y=2-x\left(1+\sqrt{3}\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2-1-\sqrt{3}=1-\sqrt{3}\end{matrix}\right.\)
