k: \(\left\{{}\begin{matrix}\dfrac{3}{4}x+y=\dfrac{1}{2}\\x+\dfrac{3}{4}y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{4}x+y=\dfrac{1}{2}\\\dfrac{3}{4}x+\dfrac{9}{16}y=\dfrac{3}{4}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{3}{4}x+y-\dfrac{3}{4}x-\dfrac{9}{16}y=\dfrac{1}{2}-\dfrac{3}{4}\\x+\dfrac{3}{4}y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{7}{16}y=\dfrac{2}{4}-\dfrac{3}{4}=-\dfrac{1}{4}\\x+\dfrac{3}{4}y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{1}{4}:\dfrac{7}{16}=-\dfrac{1}{4}\cdot\dfrac{16}{7}=-\dfrac{4}{7}\\x=1-\dfrac{3}{4}y=1-\dfrac{3}{4}\cdot\dfrac{-4}{7}=1+\dfrac{3}{7}=\dfrac{10}{7}\end{matrix}\right.\)
l: \(\left\{{}\begin{matrix}\dfrac{x+y}{3}+\dfrac{2}{3}=3\\\dfrac{4x-y}{6}+\dfrac{x}{4}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y+2=9\\\dfrac{2\left(4x-y\right)+3x}{12}=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y=7\\2\left(4x-y\right)+3x=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=7\\7x-2y=12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y=14\\7x-2y=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y+7x-2y=14+12\\x+y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9x=26\\y=7-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{26}{9}\\y=7-\dfrac{26}{9}=\dfrac{63}{9}-\dfrac{26}{9}=\dfrac{37}{9}\end{matrix}\right.\)
m: \(\left\{{}\begin{matrix}5\left(x+2y\right)-3\left(x-y\right)=99\\x-3y=7x-4y-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+10y-3x+3y=99\\x-3y-7x+4y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+13y=99\\-6x+y=-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x+39y=297\\-6x+y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+39y-6x+y=297-17\\2x+13y=99\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}40y=280\\2x=99-13y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\x=\dfrac{99-13y}{2}=\dfrac{99-91}{2}=\dfrac{8}{2}=4\end{matrix}\right.\)
n: \(\left\{{}\begin{matrix}x+y=\dfrac{4x-3}{5}\\x+3y=\dfrac{15-9y}{14}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5\left(x+y\right)=4x-3\\14\left(x+3y\right)=15-9y\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+5y-4x=-3\\14x+42y+9y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+5y=-3\\23x+42y=15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}23x+115y=-69\\23x+42y=15\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}23x+115y-23x-42y=-69-15\\x+5y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}73y=-84\\x=-3-5y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{84}{73}\\x=-3-5\cdot\dfrac{-84}{73}=\dfrac{201}{73}\end{matrix}\right.\)
