the sum of two integers is 7.

Question

the sum of two integers is 7. the larger integer is 13 more than twice the smaller integer. find both the smaller integer and the larger integer

Answer 1

Let x be the smaller integer and y be the larger integer.

The sum of the two integers is 7, which can be written as:

x + y = 7

The larger integer, y, is 13 more than twice the smaller integer, x, which can be written as:

y = 13 + 2x

So we have two equations now

1). x + y = 7

2). y = 13 + 2x

Since we know what y is in terms of x, we can plug equation (2) into equation (1):

x + (13 + 2x) = 7

Solving for x:

3x + 13 = 7

3x = -6

x = -2

Now we can find y by plugging x into the equation (1):

-2 + y = 7

y = 9

So, x = -2 and y = 9.

The smaller integer is -2 and the larger integer is 9.

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Always make sure to check your answer once you are done.

Is the sum of the two integers 7?

-2 + 9 = 7 (CHECK)

Is the larger number 13 more than twice the smaller number?

(-2 * 2) + 13 = -4 + 13 = 9 (CHECK)

Answer 2

x = first integer

2x + 13 = larger integer

sum is 7 so

x + 2x + 13 = 7

3x = -6

x = -2

larger integer = 2x + 13 = 2(-2) = 13 = 9