Ta có x/3=3y/2
nên \(\dfrac{x}{3}=\dfrac{y}{\dfrac{2}{3}}\)
\(\Leftrightarrow\dfrac{x}{3}\cdot\dfrac{1}{6}=\dfrac{y}{\dfrac{2}{3}}\cdot\dfrac{1}{6}\)
=>x/18=y/4
=>x/54=y/12
\(\dfrac{4y}{3}=\dfrac{z}{5}\)
nên \(\dfrac{y}{\dfrac{3}{4}}=\dfrac{z}{5}\)
\(\Leftrightarrow\dfrac{y}{\dfrac{3}{4}}\cdot\dfrac{1}{60}=\dfrac{z}{5}\cdot\dfrac{1}{60}\)
=>y/45=z/300
=>y/3=z/20
=>y/12=z/80
=>x/54=y/12=z/80
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{x}{54}=\dfrac{y}{12}=\dfrac{z}{80}=\dfrac{2x+3y-z}{2\cdot54+3\cdot12-80}=\dfrac{-7}{64}\)
Do đó: \(\left\{{}\begin{matrix}x=-\dfrac{189}{32}\\y=-\dfrac{21}{16}\\z=-\dfrac{35}{4}\end{matrix}\right.\)