Process of eliminiation method ? Is there a solution, infinity or no solution. I don't get it. Can anyone help me?

3r - 5s = -27
5r + 3s = 23

multiply the top by 3 and the bottom by 5 to eliminate the s's

9r-15s=-81
25r+15s=115
add the rows together
34r=34
divide both sides by 34
r=1
plugging in r=1 to either equation
5+3s=23
subtract 5 from both rows
3s=18
s=6
solution: r=1, s=6