#### Answer

$$c=2,\:b=-4,\:a=-3$$

#### Work Step by Step

Solving the system of equations using substitution, we find:
$$ 7\cdot \frac{13+2\cdot \frac{25c-154}{26}-7c}{3}-9\cdot \frac{25c-154}{26}-9c=-3 \\ c=2 \\ b=\frac{25\cdot \:2-154}{26}=-4 \\ a=\frac{13+2\left(-4\right)-7\cdot \:2}{3}=-3 $$