\(a,7x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{7}=\dfrac{x-y}{4-7}=\dfrac{-24}{-3}=8\\ \Rightarrow\left\{{}\begin{matrix}x=32\\y=56\end{matrix}\right.\\ b,\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\Rightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x+y-z}{8+12-15}=\dfrac{20}{5}=4\\ \Rightarrow\left\{{}\begin{matrix}x=32\\y=48\\z=60\end{matrix}\right.\\ c,\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{2x+3y-5z}{2\cdot2+3\cdot3-5\cdot4}=\dfrac{-21}{-7}=3\\ \Rightarrow\left\{{}\begin{matrix}x=6\\y=9\\z=12\end{matrix}\right.\)
\(d,\Rightarrow\dfrac{x}{3}=\dfrac{y}{8}=\dfrac{z}{5}=\dfrac{3x+y-2z}{3\cdot3+8-2\cdot5}=\dfrac{14}{7}=2\\ \Rightarrow\left\{{}\begin{matrix}x=6\\y=16\\z=10\end{matrix}\right.\\ e,Đặt.\dfrac{x}{2}=\dfrac{y}{3}=k\Rightarrow x=2k;y=3k\\ xy=54\Rightarrow6k^2=54\\ \Rightarrow k^2=9\\ \Rightarrow\left[{}\begin{matrix}k=3\\k=-3\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6;y=9\\x=-6;y=-9\end{matrix}\right.\\ f,Đặt.\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=k\Rightarrow x=2k;y=3k;z=4k\\ x^2-y^2+2z^2=108\\ \Rightarrow4k^2-9k^2+32k^2=108\\ \Rightarrow27k^2=108\\ \Rightarrow k^2=4\Rightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4;y=6;z=8\\x=-4;y=-6;z=-8\end{matrix}\right.\)
