\(\left\{{}\begin{matrix}3\left(x+y\right)+5\left(x-y\right)=12\\-5\left(x+y\right)+2\left(x-y\right)=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+3y+5x-5y=12\\-5x-5y+2x-2y=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}8x-2y=12\\-3x-7y=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}8x-2y=12\\3x+7y=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}24x-6y=36\\24x+56y=-96\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-62y=132\\8x-2y=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-\dfrac{66}{31}\\4x-y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{66}{31}\\4x=y+6=\dfrac{120}{31}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{30}{31}\\y=-\dfrac{66}{31}\end{matrix}\right.\)
