# The difference of 2 numbers is 3. The sum is 13. What are the numbers?

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### 2 Answers

Let the numbers be x and y.

Given the difference between the numbers is 3.

==> x - y = 3...........(1)

Also, given the sum of the numbers is 13.

==> x + y = 13...............(2)

Now we have a system of two equations and two variables.

Then, we will use the elimination or substitution method to solve.

Let us use the elimination method.

First, we will add (1) and (2).

==> 2x = 16.

Now we will divide by 2.

**==> x = 8.**

Now we will substitute in (2) to find y.

==> x+ y = 13

==> 8 + y = 13

==> y= 13-8

**==> y= 5.**

**Then, the numbers are 5 and 8.**

We'll note the numbers as a and b.

Their sum is 3:

a + b = 13

We'll change the equation in:

a = 13 - b (1)

The difference between the 2 numbers is 3:

a - b = 3 (2)

We'll substitute (1) in (2):

13 - b - b = 3

We'll combine like terms:

13 - 2b = 3

We'll subtract 13:

-2b = 3 - 13

-2b = -10

We'll divide by -2:

b = 5

We'll substitute b in (1):

a = 13 - 5

a = 8

**The values of the 2 numbers whose sum is 13 and difference is 3, are: {8 ; 5}.**