Solve by the elimination method?

3r - 5s = -16..............multiply with 5
5r + 3s = 30................multiply with 3

15r - 25s = -80
15r + 9s = 90
--------------------- minus them
-34s = -170
s=5
r= 3

9r - 15s = - 48
25r + 15s = 150-----ADD

34r = 102
r = 3

15 + 3s = 30
3s = 15
s = 5

r = 3 , s = 5

3r - 5s = -16
5(3r - 5s) = 5(-16)
15r - 25s = -80

5r + 3s = 30
3(5r + 3s) = 3(30)
15r + 9s = 90

..15r - 25s = -80
- 15r + 9s = 90
-----------------------
-34s = -170
s = -170/-34
s = 170/34
s = 5

3r - 5s = -16
3r - 5(5) = -15
3r - 25 = -16
3r = -16 + 25
3r = 9
r = 9/3
r = 3

∴ r = 3 , s = 5

3r - 5s = -16
5r + 3s = 30

multiply the first equation by 3 and the second by 5

9r - 15s = - 48
25r + 15s = 150

Add the two equations going straight down

34r = 102
r = 102/34
r = 3

sub back into one of the equations

3(3) - 5s = -16
9 - 5s = - 16
- 5s = -25
s = (-25)/-5
s = 5

r = 3.....s = 5

3r - 5s = -16
5r + 3s = 30

9r - 15s = -48
25r + 15s = 150

34r = 102

r = 3

-15r + 25s = 80
15r + 9s = 90

34s = 170

s = 5