# Ineed with my homework answer this correctly

## Answers

2 numbers can be represented by the variables x and y.

Set up a system of equations:

[tex]x + y = 37[/tex]

[tex]x - y = 31[/tex]

The two numbers added together will result in a sum of 37. However, one number subtracted from another will result in a difference of 31.

In both systems of equations, there are inverses of variable y. Therefore, we can combine the systems of equations by adding them together:

[tex](x + x) + (y - y) = (37 + 31)[/tex]

[tex]2x = 68[/tex]

Divide both sides by 2 to get x by itself:

[tex]x = 34[/tex]

One of the numbers will be 34.

Plug the value into one of the equations:

[tex]34 + y = 37[/tex]

Subtract 34 from both sides to get y by itself:

[tex]y = 3[/tex]

The two numbers that sum up to 37, with a difference of 31 between them, will be 3 and 34.

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