có \(5x=6y=>x=\dfrac{6y}{5}\)
có \(6y=8z=>z=\dfrac{6y}{8}\)
thế x,z vào \(2x+y+z=-83\)
\(=>\dfrac{12y}{5}+y+\dfrac{6y}{8}=-83=>y=-20\)
\(=>x=\dfrac{6\left(-20\right)}{5}=-24\)
\(=>z=\dfrac{6\left(-20\right)}{8}=-15\)
\(5x=6y=8z\)
nên \(\dfrac{x}{\dfrac{1}{5}}=\dfrac{y}{\dfrac{1}{6}}=\dfrac{z}{\dfrac{1}{8}}\)
hay \(\dfrac{2x}{\dfrac{2}{5}}=\dfrac{y}{\dfrac{1}{6}}=\dfrac{z}{\dfrac{1}{8}}=\dfrac{2x+y+z}{\dfrac{2}{5}+\dfrac{1}{6}+\dfrac{1}{8}}=\dfrac{-83}{\dfrac{83}{120}}=-120\)
\(\Leftrightarrow x=-24;y=-20;z=-15\)