\(\left\{{}\begin{matrix}\dfrac{-5x+2y}{3}+5=\dfrac{y+27}{4}-2x\\\dfrac{x+1}{3}+y=\dfrac{6y-5x}{7}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{4\left(-5x+2y\right)}{12}+\dfrac{60}{12}=\dfrac{3\left(y+27\right)}{12}-\dfrac{24x}{12}\\\dfrac{7\left(x+1\right)}{21}+\dfrac{21y}{21}=\dfrac{3\left(6y-5x\right)}{21}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4\left(-5x+2y\right)+60=3\left(y+27\right)-24x\\7\left(x+1\right)+21y=3\left(6y-5x\right)\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-20x+8y+60=3y+81-24x\\7x+7+21y=18y-15x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+5y=21\\22x+3y=-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}44x+55y=231\\44x+6y=-14\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}49y=245\\4x+5y=21\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\4x=21-5y=21-5\cdot5=-4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=5\\x=-1\end{matrix}\right.\)
