\(\Rightarrow-3x=-2y.\\ \Leftrightarrow3x=2y.\\ \Leftrightarrow x=\dfrac{2}{3}y.\\ 4x-3y=9.\\ \Rightarrow4.\dfrac{2}{3}y-3y=9.\\ \Leftrightarrow\dfrac{8}{3}y-3y=9.\\ \Leftrightarrow-\dfrac{1}{3}y=9.\\ \Leftrightarrow y=-27.\\ \Rightarrow x=\dfrac{2}{3}y=\dfrac{2}{3}.\left(-27\right)=-18.\)
\(\Rightarrow x=\dfrac{3}{4}y.\\ x-y=11.\\ \Rightarrow\dfrac{3}{4}y-y=11.\\ \Leftrightarrow-\dfrac{1}{4}y=11.\\ \Leftrightarrow y=-44.\\ \Rightarrow x=\dfrac{3}{4}y=\dfrac{3}{4}.\left(-44\right)=-33.\)
\(\Rightarrow x=\dfrac{4}{3}y.\\ 2x+3y=34.\\ \Rightarrow2.\dfrac{4}{3}y+3y=34.\\ \Leftrightarrow\dfrac{8}{3}y+3y=34.\\ \Leftrightarrow\dfrac{17}{3}y=34.\\ \Leftrightarrow y=6.\)
e) \(\dfrac{x}{-2}=\dfrac{y}{-3};4x-3y=9\)
Ta có \(\dfrac{x}{-2}=\dfrac{y}{-3}\Rightarrow\dfrac{4x}{-8}=\dfrac{3y}{-9}=\dfrac{4x-3y}{-8-\left(-9\right)}=\dfrac{9}{1}=9\)
\(\Rightarrow\left\{{}\begin{matrix}4x=-72\\3y=-81\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-18\\y=-27\end{matrix}\right.\)
f) \(4x=3y;x-y=11\)
Ta có \(4x=3y\Rightarrow\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{x-y}{3-4}=\dfrac{11}{-1}=-11\)
\(\Rightarrow\left\{{}\begin{matrix}x=-33\\y=-44\end{matrix}\right.\)
g) \(3x=4y;2x+3y=34\)
Ta có \(3x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{3}\)
\(\Rightarrow\dfrac{2x}{8}=\dfrac{3y}{9}=\dfrac{2x+3y}{8+9}=\dfrac{34}{17}=2\)
\(\Rightarrow\left\{{}\begin{matrix}2x=16\\3y=18\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=8\\y=6\end{matrix}\right.\)
