Linear combinations of random variables — practice question

Two matching biased triangular spinners, each with sides labelled $1$, $2$ and $3$, are spun. For each spinner, the chances of landing on the sides marked $1$, $2$ and $3$ are $p$, $q$ and $r$ respectively. The score is the total of the numbers on the sides where the spinners land. You are given that $P(\text{score is } 6) = \frac{1}{36}$ and $P(\text{score is } 5) = \frac{1}{9}$.