a: \(\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+y+2x-y=3+7\\2x-y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x=10\\y=2x-7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=2\cdot2-7=-3\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}8x-7y=5\\12x+13y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}24x-21y=15\\24x+26y=-16\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}24x-21y-24x-26y=15+16\\8x-7y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-47y=31\\8x=7y+5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{31}{47}\\x=\dfrac{7y+5}{8}=\dfrac{9}{188}\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}5x+2y=3x-1\\2x+4=3\left(x-5y\right)-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y=-1\\2x+4-3x+15y=-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y=-1\\2x+12y=-16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y-2x-12y=-1+16\\x+y=-\dfrac{1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-10y=15\\x=-\dfrac{1}{2}-y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{3}{2}\\x=-\dfrac{1}{2}+\dfrac{3}{2}=1\end{matrix}\right.\)
\(a,\left\{{}\begin{matrix}3x+y=3\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x=10\\2x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{10}{5}=2\\4-y=7\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=2\\y=7-4=3\end{matrix}\right.\\ b,\left\{{}\begin{matrix}8x-7y=5\\12x+13y=-8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}24x-21y=15\\24x+26y=-16\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}47y=-31\\8x-7y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-31}{47}\\8x+\dfrac{217}{47}=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-31}{47}\\x=\left(5-\dfrac{217}{47}\right):8=\dfrac{9}{188}\end{matrix}\right.\)
