Answer
$$r=-\frac{1}{2},\:q=\frac{1}{2},\:p=4$$
Work Step by Step
Solving the system of equations using substitution, we find:
$$ \frac{11-2r}{3}-6\left(4+7r\right)=1 \\ r=-.5 \\ q=4+7\left(-\frac{1}{2}\right)=.5 \\ p=\frac{11-2\left(-\frac{1}{2}\right)}{3}=4$$
