\(5x=8y\Rightarrow\dfrac{x}{8}=\dfrac{y}{5}=\dfrac{y-x}{5-8}=\dfrac{-12}{-3}=4\\ \Rightarrow\left\{{}\begin{matrix}x=32\\y=20\end{matrix}\right.\\ Đặt\dfrac{x}{2}=\dfrac{y}{5}=k\Rightarrow x=2k;y=5k\\ xy=90\Rightarrow10k^2=90\\ \Rightarrow k^2=9\Rightarrow\left[{}\begin{matrix}k=3\\k=-3\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=6;y=15\\x=-6;y=-15\end{matrix}\right.\\ \dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+2y-3z}{2+2\cdot3-3\cdot4}=\dfrac{-20}{-4}=5\\ \Rightarrow\left\{{}\begin{matrix}x=10\\y=15\\z=20\end{matrix}\right.\)
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