Question

\(\left\{{}\begin{matrix}\left(x-5\right)\left(y+4\right)=xy-10\\\left(x+3\right)\left(y-7\right)=xy+10\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}\left(x-5\right)\left(y+4\right)=xy-10\\\left(x+3\right)\left(y-7\right)=xy+10\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}xy+4x-5y-20=xy-10\\xy-7x+3y-21=xy+10\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}4x-5y=10\\-7x+3y=31\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}28x-35y=70\\-28x+12y=124\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-23y=194\\4x-5y=10\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=\dfrac{-194}{23}\\4x=10+5y=-\dfrac{740}{23}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=-\dfrac{194}{23}\\x=-\dfrac{185}{23}\end{matrix}\right.\)