Chapter 8 - Systems of Linear Equations and Problem Solving - 8.4 Systems of Equations in Three Variables - 8.4 Exercise Set - Page 538: 19

$$c=-2,\:b=-14,\:a=21$$

Solving the system of equations using substitution, we find: $$ 2\left(5-\left(3c-8\right)-c\right)+3\left(3c-8\right)-2c=4 \\ c=-2 \\ b=3\left(-2\right)-8=-14 \\ a=5-\left(-14\right)-\left(-2\right)=21 $$