Chapter 8 - Systems of Linear Equations and Problem Solving - 8.4 Systems of Equations in Three Variables - 8.4 Exercise Set - Page 537: 14

$$z=2,\:y=1,\:x=3$$

Solving the system of equations using substitution, we find: $$3\cdot \frac{5+3\cdot \frac{-5z+13}{3}-z}{2}-\frac{-5z+13}{3}+2z=12 \\ z=2 \\ y=\frac{-5\cdot \:2+13}{3} \\ y=1 \\ x=\frac{5+3\cdot \:1-2}{2}=3$$