Answer
$$r=6,\:q=-1,\:p=-\frac{1}{2}$$
Work Step by Step
Solving the system of equations using substitution, we find:
$$ 2\cdot \frac{3-\left(-\frac{-r+9}{3}\right)-r}{4}+2\left(-\frac{-r+9}{3}\right)-r=-9\\ r=6 \\ q=-\frac{-6+9}{3}\\ q=-1\\ p=\frac{3-\left(-1\right)-6}{4}\\ p=-\frac{1}{2}$$