\(a)\left\{{}\begin{matrix}4x+3y=-7\\2x-5y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+3y=-7\\4x-10y=32\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}13y=-39\\2x-5y=16\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{39}{13}=-3\\2x-5\cdot-3=16\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}y=3\\2x=16-15=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3\\x=\dfrac{1}{2}\end{matrix}\right.\\ b)\left\{{}\begin{matrix}x-2y=1\\2x+y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-4y=2\\2x+y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5y=5\\2x+y=7\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{5}{5}=1\\2x+1=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\2x=7-1=6\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{6}{2}=3\end{matrix}\right.\)
\(c)\left\{{}\begin{matrix}7x-2y=1\\3x+y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x-2y=1\\6x+2y=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+y=6\\13x=13\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}3+y=6\\x=\dfrac{13}{13}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=6-3=3\\x=1\end{matrix}\right.\\ d)\left\{{}\begin{matrix}2x-5y=-9\\4x+3y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x-10y=-18\\4x+3y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13y=13\\4x+3y=-5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{13}{13}=1\\4x+3=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\4x=-8\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=1\\x=-\dfrac{8}{4}=-2\end{matrix}\right.\)
