a: \(\left\{{}\begin{matrix}\dfrac{x}{y}=\dfrac{2}{3}\\x+y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x=2y\\x=-y+1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-y+1\\3\left(-y+1\right)-2y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-y+1\\-3y+3-2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-y+1\\3-5y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5y=3\\x=-y+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{3}{5}\\x=-\dfrac{3}{5}+1=\dfrac{2}{5}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}\dfrac{3}{2}x+2y=0\\\dfrac{x+y}{2}-\dfrac{2y}{3}=\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+4y=0\\3\left(x+y\right)-4y=15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+4y=0\\3x-y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3x-15\\3x+4\left(3x-15\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}15x-60=0\\y=3x-15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=3\cdot4-15=12-15=-3\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)x-y=\sqrt{2}\\x+\left(\sqrt{2}+1\right)y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)x-\left(\sqrt{2}+1\right)y=\sqrt{2}\left(\sqrt{2}+1\right)\\x+\left(\sqrt{2}+1\right)y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-\left(\sqrt{2}+1\right)y=2+\sqrt{2}\\x+\left(\sqrt{2}+1\right)y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-\left(\sqrt{2}+1\right)y+x+\left(\sqrt{2}+1\right)y=3+\sqrt{2}\\\left(\sqrt{2}-1\right)x-y=\sqrt{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=3+\sqrt{2}\\y=\left(\sqrt{2}-1\right)x-\sqrt{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3+\sqrt{2}}{2}\\y=\left(\sqrt{2}-1\right)\cdot\dfrac{3+\sqrt{2}}{2}-\sqrt{2}=-\dfrac{1}{2}\end{matrix}\right.\)
