Call equations A, B and C. 2A+C: 16q+9s=17. Call this equation D.
3A+B=20q+5s=15 or 4q+s=3. Call this equation E.
D-4E: 5s=5, so s=1. Therefore, 4q=3-s=2, so q=1/2.
From A, r=6q+2s-8=3+2-8=-3.
The solution is q=1/2, r=-3, s=1.
Check by substitution: A: 3+3+2=8; B: 1-9-1=-9; C: 2-6+5=1. All correct.