Ta có:
\(\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{1}{3}.\frac{x}{3}=\frac{1}{3}.\frac{y}{4}\Rightarrow\frac{x}{9}=\frac{y}{12}\) (1)
\(\frac{y}{3}=\frac{z}{5}\Rightarrow\frac{1}{4}.\frac{y}{3}=\frac{1}{4}.\frac{z}{5}\Rightarrow\frac{y}{12}=\frac{z}{20}\) (2)
Từ (1) và (2) \(\Rightarrow\frac{x}{9}=\frac{y}{12}=\frac{z}{20}=\frac{2x}{18}=\frac{3y}{36}=\frac{2x-3y-z}{18-36-20}=\frac{50}{-38}\Rightarrow\left\{{}\begin{matrix}\frac{x}{9}=\frac{50}{-38}\Rightarrow x=\frac{225}{-19}\\\frac{y}{12}=\frac{50}{-38}\Rightarrow y=\frac{300}{-19}\\\frac{z}{20}=\frac{50}{-38}\Rightarrow z=\frac{500}{-19}\end{matrix}\right.\)
b)Ta có:
\(2x=3y\Rightarrow\frac{x}{3}=\frac{y}{2}\Rightarrow\frac{1}{7}.\frac{x}{3}=\frac{1}{7}.\frac{y}{2}\Rightarrow\frac{x}{21}=\frac{y}{14}\)(1)
\(5y=7z\Rightarrow\frac{y}{7}=\frac{z}{5}\Rightarrow\frac{1}{2}.\frac{y}{7}=\frac{1}{2}.\frac{z}{5}\Rightarrow\frac{y}{14}=\frac{z}{10}\) (2)
Từ (1) và (2)
\(\Rightarrow\frac{x}{21}=\frac{y}{14}=\frac{z}{10}=\frac{3x}{63}=\frac{5z}{50}=\frac{7y}{98}=\frac{3x+5z-7y}{63+50-98}=\frac{30}{15}=2\Rightarrow\left\{{}\begin{matrix}\frac{x}{21}=2\Rightarrow x=42\\\frac{y}{14}=2\Rightarrow y=28\\\frac{z}{10}=2\Rightarrow z=20\end{matrix}\right.\)
