a
Có \(\dfrac{x}{4}=\dfrac{3y}{9}=\dfrac{4z}{36}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{4}=\dfrac{3y}{9}=\dfrac{4z}{36}=\dfrac{x-3y+4z}{4-9+36}=\dfrac{62}{31}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.4=8\\y=\dfrac{2.9}{3}=6\\z=\dfrac{2.36}{4}=18\end{matrix}\right.\)
b
\(\dfrac{x}{y}=\dfrac{3}{4}\Rightarrow\dfrac{x}{3}=\dfrac{y}{4}\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}\)
\(\dfrac{y}{z}=\dfrac{5}{7}\Rightarrow\dfrac{y}{5}=\dfrac{z}{7}\Rightarrow\dfrac{y}{20}=\dfrac{z}{28}\)
\(\Rightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{28}=\dfrac{2x+3y-z}{2.15+3.20-28}=\dfrac{186}{62}=3\)
\(\Rightarrow\left\{{}\begin{matrix}x=3.15=45\\y=3.20=60\\z=3.28=84\end{matrix}\right.\)
