a. \(\frac{x}{3}=\frac{z}{8}\)
và \(-6y=7z\Rightarrow\frac{y}{7}=\frac{z}{-6}\)
\(\frac{x}{3}=\frac{z}{8}\Rightarrow\) \(\frac{x}{3.3}=\frac{z}{8.3}\Rightarrow\frac{x}{9}=\frac{z}{24}\)
\(-6y=7z\Rightarrow\frac{y}{7}=\frac{z}{-6}\Rightarrow\frac{y}{-7.4}=\frac{z}{6.4}\Rightarrow\frac{y}{-28}=\frac{z}{24}\)
=> \(\frac{x}{9}=\frac{y}{-28}=\frac{z}{24}\)
Áp dụng dãy tỉ số bằng nhau: \(\frac{x}{9}=\frac{y}{-28}=\frac{z}{24}=\frac{2x-9y}{2.9-9\left(-28\right)}=\frac{2}{270}=\frac{1}{135}\)
=> \(\frac{x}{9}=\frac{1}{135}\Rightarrow x=\frac{1}{15}\)
\(\frac{y}{-28}=\frac{1}{135}\Rightarrow y=-\frac{28}{135}\)
\(\frac{z}{24}=\frac{1}{135}\Rightarrow z=\frac{8}{45}\)
b) Áp dụng dãy tỉ số bằng nhau ta có:
\(\frac{x}{3}=\frac{y}{3}=\frac{z}{7}=\frac{x+2y+3z}{3+2.3+3.7}=\frac{19}{30}\)
=> \(\frac{x}{3}=\frac{19}{30}\Rightarrow x=\frac{19}{10}\)
\(\frac{y}{3}=\frac{19}{30}\Rightarrow y=\frac{19}{10}\)
\(\frac{z}{7}=\frac{19}{30}\Rightarrow z=\frac{133}{30}\)
