a: \(\left\{{}\begin{matrix}2x-11y=-7\\10x+11y=31\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-11y+10x+11y=-7+31\\2x-11y=-7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}12x=24\\11y=2x+7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\11y=2\cdot2+7=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}4x+7y=16\\4x-3y=-24\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+7y-4x+3y=16+24\\4x+7y=16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10y=40\\4x=16-7y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=4\\4x=16-28=-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-3\\y=4\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}\left(x+14\right)\left(y-2\right)=xy\\\left(x-4\right)\left(y+1\right)=xy\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy-2x+14y-28=xy\\xy+x-4y-4=xy\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x+14y=28\\x-4y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x+7y=14\\x-4y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x+7y+x-4y=14+4\\x-4y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3y=18\\x=4y+4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=6\\x=4\cdot6+4=28\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}2x-3y=-5\\-3x+4y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x-9y=-15\\-6x+8y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-9y-6x+8y=-15+4\\3x-4y=-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-y=-11\\3x=4y-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=11\\3x=4\cdot11-2=42\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=14\\y=11\end{matrix}\right.\)
e: \(\left\{{}\begin{matrix}2x+4=0\\4x+2y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-4\\4x+2y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\2y=-3-4x=-3-4\cdot\left(-2\right)=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{5}{2}\\x=-2\end{matrix}\right.\)
f: \(\left\{{}\begin{matrix}2x+4=y\\x+2y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2x+4\\x+2\left(2x+4\right)=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2x+4\\5x+8=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2x+4\\5x=-11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{11}{5}\\y=2\cdot\dfrac{-11}{5}+4=\dfrac{-22}{5}+4=-\dfrac{2}{5}\end{matrix}\right.\)
g: \(\left\{{}\begin{matrix}\left(x-15\right)\left(y+2\right)=xy\\\left(x+15\right)\left(y-1\right)=xy\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy+2x-15y-30=xy\\xy-x+15y-15=xy\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-15y=30\\-x+15y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-15y-x+15y=30+15\\x-15y=-15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=45\\15y=x+15=60\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=45\\y=4\end{matrix}\right.\)
