Question

\(\dfrac{x}{3}\)=\(\dfrac{y}{4}\)=\(\dfrac{z}{6}\),x+2y=3z-14 

sos

Answer 1

\(x+2y=3z-14\\ =>x+2y-3z=-14\)

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{6}\\ =>\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{18}\)

áp dụng tính chất dãy tỉ số bằng nhau ta có

\(\dfrac{x}{3}=\dfrac{2y}{8}=\dfrac{3z}{18}=\dfrac{x+2y-3z}{3+8-18}=\dfrac{-14}{-7}=2\)

\(=>x=2\cdot3=6\\ y=2\cdot4=8\\ z=2\cdot6=12\)

Answer 2

\(x+2y=3z-14\\ =>x+2y-3z=-14\)

Áp dụng tính chất dãy tỉ số bằng nhau :

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{6}=\dfrac{x+2y-3z}{3+2.4-3.6}=\dfrac{-14}{-7}=2\\ =>\left\{{}\begin{matrix}x=2.3=6\\y=2.4=8\\z=2.6=12\end{matrix}\right.\)