\(x:y:z=3:5:\left(-2\right)\)
\(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}=\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{-6}=\dfrac{5x+y-3z}{15-5-6}=-\dfrac{16}{4}=-4\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{3}=-4\Rightarrow x=\left(-4\right).3=-12\\\dfrac{y}{5}=-4\Rightarrow y=\left(-4\right).5=-20\\\dfrac{z}{-2}=-4\Rightarrow z=\left(-4\right).\left(-2\right)=8\end{matrix}\right.\)
Ta có: \(\dfrac{x}{3}=\dfrac{y}{5}=\dfrac{z}{-2}\)
nên \(\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{-6}\)
mà 5x-y+3z=-16
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{5x}{15}=\dfrac{y}{5}=\dfrac{3z}{-6}=\dfrac{5x-y+3z}{15-5-6}=-\dfrac{16}{4}=-4\)
Do đó: x=-12; y=-20; z=8
