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Answer: B) 24</h3>
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Explanation:
Add the left hand sides of the two equations to get (4r+7s)+(r-2s) = 5r+5s
Do the same for the right hand sides of the two equations 23+17 = 40
After adding the equations, we end up with 5r+5s = 40 which is the same as 5(r+s) = 40
Next, divide both sides by 5 to lead to r+s = 8
Finally, multiply both sides by 3 to end up with 3(r+s) = 24 which is the same as 3r+3s = 24
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An alternative is to solve r-2s = 17 for r to get r = 2s+17. Then plug this into 4r+7s = 23 getting 4(2s+17)+7s = 23. This solves to...
4(2s+17)+7s = 23
8s+68+7s = 23
15s+68 = 23
15s = 23-68
15s = -45
s = -45/15
s = -3
Which means,
r = 2s+17
r = 2(-3)+17
r = 11
and therefore,
3r+3s = 3(-3)+3(11) = -9+33 = 24
