b) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{9}{9}=1\)
\(\Rightarrow\left\{{}\begin{matrix}x=1.2=2\\y=1.3=3\\z=1.4=4\end{matrix}\right.\)
b) \(\dfrac{x}{2}=\dfrac{y}{5}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=2k\\y=5k\end{matrix}\right.\)
\(\Rightarrow xy=10k^2=10\Rightarrow k=\pm1\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=2\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=-2\\y=-5\end{matrix}\right.\end{matrix}\right.\)
d) \(\dfrac{x}{4}=\dfrac{y}{5}=k\)
\(\Rightarrow\left\{{}\begin{matrix}x=4k\\y=5k\end{matrix}\right.\)
\(\Rightarrow xy=20k^2=20\Rightarrow k=\pm1\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=4\\y=5\end{matrix}\right.\\\left\{{}\begin{matrix}x=-4\\y=-5\end{matrix}\right.\end{matrix}\right.\)
a) \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{2y}{6}=\dfrac{3z}{12}=\dfrac{x+2y-3z}{2+6-12}=\dfrac{-20}{-4}=5\)
\(\Rightarrow\left\{{}\begin{matrix}x=5.2=10\\y=5.3=15\\z=5.4=20\end{matrix}\right.\)
