\(\left\{{}\begin{matrix}\left(x-1\right)^2+\left(y-3\right)^2=\left(x+2\right)^2+\left(y-4\right)^2\\\left(2x+1\right)^2-3\left(y-1\right)^2=\left(2x+3\right)^2-3\left(y-3\right)^2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x^2-2x+1+y^2-6y+9=x^2+4x+4+y^2-8y+16\\4x^2+4x+1-3\left(y^2-2y+1\right)=4x^2+12x+9-3\left(y^2-6y+9\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x-6y+10=4x-8y+20\\4x+1+6y-3=12x+9+18y-27\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-6x+2y=10\\-8x-12y=-18-1+3=-18+2=-16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-3x+y=5\\2x+3y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-9x+3y=15\\2x+3y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-9x+3y-2x-3y=15-4\\2x+3y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-11x=11\\3y=4-2x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1\\3y=4-2\cdot\left(-1\right)=4+2=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1\\y=2\end{matrix}\right.\)
