elimination method really confuses me.

Question

solve by elimination method
5r -3s = 17
3r + 5s =17

A. solution is ______ (ordered pair, integer or fraction)
B. Infinitely many
C. No Solution

Answer 1

try to get either the x or the y coefficients to be alike
in this case I will get the y's to have a 15 in front

so multiply the first by 5 and the second by 3 to get

25r - 15s = 85
9r + 15s = 51

add them
34r = 136
r = 136/34 = 4

back in second, (or first)
3(4) + 5s = 17

12 + 5s = 17
5s = 5
s = 1

Answer 2

thank you so much, i was not even close

Answer 3

4x-3y=-4. 3x=2y-4

Answer 4

2r+3s=29,3r+2s=16