\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\Leftrightarrow\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}=\dfrac{3x-2y+4z}{3\cdot\dfrac{3}{2}-2\cdot\dfrac{4}{3}+4\cdot\dfrac{5}{4}}=\dfrac{-164}{\dfrac{41}{6}}=-24\\ \Leftrightarrow\left\{{}\begin{matrix}x=-24\cdot\dfrac{3}{2}=-36\\y=-24\cdot\dfrac{4}{3}=-32\\z=-24\cdot\dfrac{5}{4}=-30\end{matrix}\right.\)
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