use the substitution method?

Question

use the substitution method to solve
r-8s=-20
-r-9s=-31

Answer 1

-r = 9s - 31, r = 31 - 9s

(31 - 9s) - 8s = - 20
31 -9s -8s = -20
31 - 17s = -20
-17s = -51
s = 3

Answer 2

r-8s=-20
-r-9s=-31

To use the substitution method, you need to have something to substitute.
Solve one of the equations for one of the variables.
r-8s=-20
Add 8s to both sides and you get
r = 8s-20
Now substitute the right side of that equation into the second equation
-r - 9s = -31 becomes
-(8s - 20) -9s = -31
-8s +20 - 9s = - 31
-17s +20 = -31
-17s = -51
s = -51/-17 = 3

Earlier we figured out r in terms of s. We now have s = 3, so, substituting again,
r = 8s-20
Substituting we get
r = 8(3) - 20 = 24 - 20 = 4. So r = 4

Do these values satisfy both equations?
r-8s=-20?
(4) - 8(3) = 4 - 24 = - 20... kind of expected that.

-r-9s=-31?
-(4) - 9(3) = -4 - 27 = -31. Checks.

Answer 3

r = 8s - 20
- (8s - 20) - 9s = - 31
-8s + 20 - 9s = - 31
- 17s = - 51
17s = 51
s = 3
r - 24 = - 20
r = 4
Solution is r = 4, s = 3

Answer 4

Nick k's answer is spot on!