Chapter 8 - Systems of Linear Equations and Problem Solving - 8.4 Systems of Equations in Three Variables - 8.4 Exercise Set - Page 538: 27

$$c=-\frac{5}{6},\:b=\frac{2}{3},\:a=\frac{1}{2}$$

Solving the system of equations using substitution, we find: $$ 6\left(-\frac{-6c-17}{18}\right)+6c=-1\\ c=-\frac{5}{6}\\ b=-\frac{-6\left(-\frac{5}{6}\right)-17}{18}=\frac{2}{3} \\ a=\frac{8-9\cdot \frac{2}{3}}{4}=.5$$