\(\left\{{}\begin{matrix}3x=4y\\5x=6z\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{4}=\dfrac{y}{3}\\\dfrac{x}{6}=\dfrac{z}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{12}=\dfrac{y}{9}\\\dfrac{x}{12}=\dfrac{z}{10}\end{matrix}\right.\Leftrightarrow\dfrac{x}{12}=\dfrac{y}{9}=\dfrac{z}{10}\)
\(\Leftrightarrow\dfrac{x}{12}=\dfrac{2y}{18}=\dfrac{3z}{30}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{12}=\dfrac{2y}{18}=\dfrac{3z}{30}=\dfrac{x+2y+3z}{12+18+30}=\dfrac{10}{60}=\dfrac{1}{6}\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{12}=\dfrac{1}{6}\\\dfrac{y}{9}=\dfrac{1}{6}\\\dfrac{z}{10}=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=\dfrac{3}{2}\\z=\dfrac{5}{3}\end{matrix}\right.\)
