\(\left\{{}\begin{matrix}\left(x-1\right)^2-\left(y+1\right)^2=0\\x+3y-5=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(x-1-y-1\right)\left(x-1+y+1\right)=0\\x+3y-5=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left(x-y-2\right)\left(x+y\right)=0\\x+3y-5=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y-2=0\\x+3y-5=0\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=0\\x+3y-5=0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x-y=2\\x+3y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=0\\x+3y=5\end{matrix}\right.\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}\left\{{}\begin{matrix}-4y=-3\\x-y=2\end{matrix}\right.\\\left\{{}\begin{matrix}-2y=-5\\x+y=0\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=\dfrac{3}{4}\\x=y+2=\dfrac{3}{4}+2=\dfrac{11}{4}\end{matrix}\right.\\\left\{{}\begin{matrix}y=\dfrac{5}{2}\\x=-\dfrac{5}{2}\end{matrix}\right.\end{matrix}\right.\)
