$a)\frac{x}{3}=\frac{y}{5}=\frac{z}{-2}\Leftrightarrow \frac{5x}{15}=\frac{y}{5}=\frac{3z}{-6}$$\Leftrightarrow \frac{5x-y+3z}{15-5-6}=\frac{-16}{4}=4\Rightarrow x=12 ,y=20, z=-8$
$b) x=\frac{3}{2}y , z=\frac{5}{7}y\Rightarrow 3.\frac{3}{2}y-7y+5.\frac{5}{7}y=30\Leftrightarrow y=28\Rightarrow x=42, z=20$