Question

Two numbers add up to 23. 7 times the difference of the two numbers is 21. What are the two numbers?

Define the variables: let x = first number, let y = second number
Equation 1:
Equation 2:

Solve the system:

1st number:
2nd number:
Please show work on how to get the answers. Thanks!

Answer 1

10 and 13

Explanation:

x + y = 23 . . . . . . the two numbers add up to 23

7(y -x) = 21 . . . . . 7 times their difference is 21

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Divide the second equation by 7:

y - x = 3

Add x:

y = 3 + x

Put that in the first equation in place of y

x + (3 +x) = 23

2x +3 = 23 . . . . . . . collect terms

2x = 20 . . . . . . . . . .subtract 3

x = 10 . . . . . . . . . . . . divide by 2

y = 3 +10 = 13 . . . . . .use the equation for y to find y

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1st number: 10

2nd number: 13