\(2x=3y=4z\Rightarrow\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}\)
Áp dụng tcdtsbn:
\(\dfrac{x}{6}=\dfrac{y}{4}=\dfrac{z}{3}=\dfrac{y+x}{4+3}=\dfrac{-14}{7}=-2\\ \Rightarrow\left\{{}\begin{matrix}x=-12\\y=-8\\z=-6\end{matrix}\right.\)
\(2x=3y=4z\Rightarrow\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{4}}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{\dfrac{1}{2}}=\dfrac{y}{\dfrac{1}{3}}=\dfrac{z}{\dfrac{1}{4}}=\dfrac{y+z}{\dfrac{1}{3}+\dfrac{1}{4}}=\dfrac{-14}{\dfrac{7}{12}}-24\)
\(\dfrac{x}{\dfrac{1}{2}}=-24\Rightarrow x=-12\\ \dfrac{y}{\dfrac{1}{3}}=-24\Rightarrow y=-8\\ \dfrac{z}{\dfrac{1}{4}}=-24\Rightarrow z=-6\)
