Lời giải:
$2x=3y; 5y=7z\Rightarrow \frac{x}{3}=\frac{y}{2}; \frac{y}{7}=\frac{z}{5}$
$\Rightarrow \frac{x}{21}=\frac{y}{17}=\frac{z}{10}$
Đặt $\frac{x}{21}=\frac{y}{17}=\frac{z}{10}=k$
$\Rightarrow x=21k; y=17k; z=10k$.
Khi đó:
$3x-7y+5z=-30$
$3.21k-7.17k+5.10k=-30$
$-6k=-30$
$k=5$
$\Rightarrow x=21k=21.5=105; y=17.5=85; z=10.5=50$