Solve using the elimination method.

2r - 5s = - 14

5r + 2s = 23

Since you can't multiply either equation by a single number to make the r's or s's cancel out you need to multiply both equations.

I'm going to make the r's cancel out by multiplying the top equation by 5 and the bottom by - 2

5 (2r - 5s = - 14)

-2 (5r + 2s = 23)

Once I multiply I have

10r - 25s = - 70

-10r - 4s = - 46

Now add straight down, and you are left with:

-29s = - 116

To get s by itself now you need to divide both sides by - 29

-29s = - 116

-29 - 29

And your result is s = 4

To find the value of r, substitute s = 4 into one of the original equations and solve for r.

2r - 5 (4) = - 14

2r - 20 = - 14

+ 20 + 20

2r = 6

so r = 3

So your solution is s=4 and r = 3