SOLUTION: the sum of two numbers is 13. two times the first number minus three times the second number is 1. if you let x stand for the first number and y for the second number, what are the

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Question 255923: the sum of two numbers is 13. two times the first number minus three times the second number is 1. if you let x stand for the first number and y for the second number, what are the two numbers
Answer by EMStelley(208) (Show Source):
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If our two numbers are x and y, to do this problem we just take it one sentence at a time.
"the sum of two numbers is 13"
This tells us that when you add our two numbers you get 13. So we have:
x+y=13
"two times the first number minus three times the second number is 1"
Two times the first number would be represented by 2x and three times the second number is represented by 3y. So we have:
2x-3y=1
So we have a system of equations:

Let's use the addition method to solve this system. If we multiply the first equation by 3 we will be able to eliminate the y's.

Now we add:

And using our first equation we have that y must be 5. So our two numbers are 8 and 5.