a: \(\left\{{}\begin{matrix}3\left(x-y\right)-5\left(x+2y\right)=99\\x-3y=7x-4y-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-3y-5x-10y=99\\x-3y-7x+4y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x-13y=99\\-6x+y=-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-6x-39y=297\\-6x+y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-6x-39y+6x-y=297+17\\y=6x-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-40y=314\\6x-17=y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-7,85\\6x=17-7,85=9,15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-7,85\\x=1,525\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}-2\left(x-1\right)-3\left(y+4\right)=-38\\y\left(2-x\right)+x\left(y+1\right)=17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x+2-3y-12=-38\\2y-xy+xy+x=17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x-3y=-38+12-2=-26-2=-28\\x+2y=17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+3y=28\\2x+4y=34\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+4y-2x-3y=34-28\\x+2y=17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=6\\x=17-2\cdot6=17-12=5\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}\dfrac{x-5y}{4}-\dfrac{3x-2y}{3}=\dfrac{-25}{24}\\\dfrac{5x+3y}{8}+\dfrac{x-6y}{5}=\dfrac{33}{80}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3\left(x-5y\right)-4\left(3x-2y\right)}{12}=\dfrac{-25}{24}\\\dfrac{5\left(5x+3y\right)+8\left(x-6y\right)}{40}=\dfrac{33}{80}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3x-15y-12x+8y}{12}=\dfrac{-25}{24}\\\dfrac{25x+9y+8x-48y}{40}=\dfrac{33}{80}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-9x-7y=-\dfrac{25}{2}\\33x-39y=\dfrac{33}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{201}{194}\\y=\dfrac{44}{97}\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}\left(x-1\right)\left(y-2\right)=\left(x+2\right)\left(y-1\right)\\\left(x-4\right)\left(y+7\right)=\left(x-3\right)\left(y+4\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy-2x-y+2=xy-x+2y-2\\xy+7x-4y-28=xy+4x-3y-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x-y+x-2y=-2-2\\7x-4y-4x+3y=-12+28\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+3y=4\\3x-y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+9y=12\\3x-y=16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+9y-3x+y=12-16\\x+3y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10y=-4\\x=4-3y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{2}{5}\\x=4-3\cdot\dfrac{-2}{5}=4+\dfrac{6}{5}=\dfrac{26}{5}\end{matrix}\right.\)
