SOLUTION: Hi- I know the answer to the problem. 7, 8 but I do not know how to come up with the equation or show how to solve it. HELP The sum of two numbers is 15. Three times one

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Question 102863This question is from textbook algebra structure and method book1
: Hi-
I know the answer to the problem. 7, 8 but I do not know how to come up with the equation or show how to solve it. HELP
The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers.
This question is from textbook algebra structure and method book1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers.
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x+y = 15
3x+11 = 5y
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Rearrange:
1x +1y = 15
3x -5y = -11
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Multiply thru 1st by 3 to get:
3x+3y = 45
3x-5y = -11
-----------------
Subtract 2nd from 1st to get:
8y = 56
y = 7 (one of the numbers)
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Substitute into x+y=15 to solve for x:
x+7=15
x = 8 (the other number)
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Cheers,
Stan H.