a: \(\left\{{}\begin{matrix}x+2y=8\\\dfrac{1}{2}x-y=18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=8-2y\\\dfrac{1}{2}\left(8-2y\right)-y=18\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=8-2y\\4-y-y=18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=8-2y\\4-2y=18\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2y=4-18=-14\\x=8-2y=8-\left(-14\right)=8+14=22\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-7\\x=22\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}0,2x+0,5y=0,7\\4x+10y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+5y=7\\4x+10y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-5y+7\\2\cdot\left(-5y+7\right)+10y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=-5y+7\\-10y+14+10y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}14=9\left(vôlý\right)\\x=\dfrac{-5y+7}{2}\end{matrix}\right.\)
=>Hệ vô nghiệm
c: \(\left\{{}\begin{matrix}-2x+3y=1\\\dfrac{1}{3}x-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-2x=1-3y\\\dfrac{1}{3}x-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1-3y}{-2}=\dfrac{3y-1}{2}\\\dfrac{1}{3}\left(\dfrac{3y-1}{2}\right)-\dfrac{1}{2}y=-\dfrac{1}{6}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{3y-1}{2}\\\dfrac{3y-1}{6}-\dfrac{3y}{6}=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3y-1-3y}{6}=-\dfrac{1}{6}\\x=\dfrac{3y-1}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-\dfrac{1}{6}=-\dfrac{1}{6}\\x=\dfrac{3y-1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\in R\\x=\dfrac{3y-1}{2}\end{matrix}\right.\)