Ta có:
\(\left\{{}\begin{matrix}2x=3y\Rightarrow\frac{x}{3}=\frac{y}{2}\Rightarrow\frac{1}{7}.\frac{x}{3}=\frac{1}{7}.\frac{y}{2}\Rightarrow\frac{x}{21}=\frac{y}{14}\\5x=7z\Rightarrow\frac{x}{7}=\frac{z}{5}\Rightarrow\frac{1}{3}.\frac{x}{7}=\frac{1}{3}.\frac{z}{5}\Rightarrow\frac{x}{21}=\frac{z}{15}\end{matrix}\right.\)
\(\Rightarrow\frac{x}{21}=\frac{y}{14}=\frac{z}{15}=\frac{3x}{63}=\frac{7y}{98}=\frac{5z}{75}=\frac{3x-7y+5z}{63-98+75}=\frac{30}{40}=\frac{3}{4}\Rightarrow\left\{{}\begin{matrix}x=\frac{63}{4}\\y=\frac{21}{2}\\z=\frac{45}{4}\end{matrix}\right.\)