2r+3s=16

3r+2s=16

I would use elimination:

1st one times 2 : ---> 4r + 6s = 32
2nd one times 3: --> 9r + 6s = 48
subtract them .....
5r = 16
r = 16/5

back to 2r+3s=16
32/5 + 3s = 16
times 5
32 + 15s = 80
s = 80/32 = 16/5