Ta có : \(6x=4y\Rightarrow\frac{x}{4}=\frac{y}{6}\)(*)
\(4y=3z\Rightarrow\frac{y}{3}=\frac{z}{4}\)(**)
(*) => \(\frac{x}{12}=\frac{y}{18}\)(***)
(**) => \(\frac{y}{18}=\frac{z}{24}\)(****)
Từ (***) ; (****) suy ra : \(\frac{x}{12}=\frac{y}{18}=\frac{z}{24}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có :
\(\frac{x}{12}=\frac{y}{18}=\frac{z}{24}=\frac{2x+3y-5z}{2.12+3.18-5.24}=-\frac{21}{-42}=\frac{1}{2}\)
\(\Rightarrow x=6;y=9;z=12\)
\(6x=4y=3z=t\Leftrightarrow x=\frac{t}{6},y=\frac{t}{4},z=\frac{t}{3}\).
\(2x+3y-5z=\frac{t}{3}+\frac{3t}{4}-\frac{5t}{3}=-\frac{7}{12}t=-21\Leftrightarrow t=36\)
\(\Rightarrow\hept{\begin{cases}x=\frac{36}{6}=6\\y=\frac{36}{4}=9\\z=\frac{36}{3}=12\end{cases}}\).
