Question 62
Find all quadruples $(p, q, r, s)$ of primes that satisfy the following system of equations:
$$
\begin{cases} 6p + 5q + 5r + 3s = 130 \\ 3p + 3q + 5r + 6s = 130 \end{cases}
$$
$$
\begin{cases} 6p + 5q + 5r + 3s = 130 \\ 3p + 3q + 5r + 6s = 130 \end{cases}
$$