10: \(\left\{{}\begin{matrix}\left(x-1\right)\left(y-2\right)=\left(x+1\right)\left(y-3\right)\\\left(x-5\right)\left(y+4\right)=\left(x-4\right)\left(y+1\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy-2x-y+2=xy-3x+y-3\\xy+4x-5y-20=xy+x-4y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x-y+2=-3x+y-3\\4x-5y-20=x-4y-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x-y+3x-y=-3-2\\4x-5y-x+4y=-4+20\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-2y=-5\\3x-y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-2y=-5\\6x-2y=32\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-5x=-37\\3x-y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{37}{5}\\y=3x-16=\dfrac{111}{5}-16=\dfrac{31}{5}\end{matrix}\right.\)
11: \(\left\{{}\begin{matrix}3\left(x-7\right)-6\left(x-y+1\right)=0\\4\left(x-1\right)+2\left(x-2y+7\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-7-2\left(x-y+1\right)=0\\2\left(x-1\right)+x-2y+7=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-7-2x+2y-2=0\\2x-2+x-2y+7=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x+2y=9\\3x-2y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=4\\-x+2y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\2y=9+x=9+2=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=\dfrac{11}{2}\end{matrix}\right.\)
12: \(\left\{{}\begin{matrix}5\left(x+2y\right)-3\left(x-y\right)=99\\x-3y=7x-4y-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+10y-3x+3y=99\\x-3y-7x+4y=-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+13y=99\\-6x+y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+39y=297\\-6x+y=-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}40y=280\\-6x+y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\-6x=-17-y=-24\end{matrix}\right.\)
=>x=4 và y=7
