The largest of 2 integers is one more than three times the smaller. if the sum of the two integers is 37

The two integers are 28 and 9

Explanation:

Let's call the two integers x and y.

We have:

- The largest of the 2 integers is one more than three times the smaller: this means

x = 3y + 1 (1)

- The sum of the two integers is 37:

x + y = 37 (2)

It's a system of two equations that we can solve. Substituting directly (1) into (2),

3y + 1 + y = 37

4y + 1 = 37

4y = 36

y = 9

And so,

x = 3y + 1 = 3(9) + 1 = 27 +1 = 28

So the two integers are 28 and 9.

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