# The sum of two numbers is 18 and their difference is two. What are the two numbers?

## Question:

The sum of two numbers is 18 and their difference is two. What are the two numbers?

## Elimination Method:

In the elimination method, we solve a system of two equations of two variables by adding or subtracting the equations. By doing so, we get a linear equation in one variable, which we can solve easily.

## Answer and Explanation:

Let us assume the two numbers to be {eq}x {/eq} and {eq}y {/eq}.

The sum of the two numbers is 18. So we get: {eq}x+y=18\,\,\,\rightarrow (1) {/eq}.

The difference between the two numbers is 2. So we get: {eq}x-y=2\,\,\,\rightarrow (2) {/eq}

Adding (1) and (2):

$$x+y+x-y =18+2 \\ 2x = 20\\ \text{Dividing both sides by 2}, \\ \boxed{\mathbf{x=10}} $$

Substitute this in (1):

$$10+y=18 \\ \text{Subtracting 10 from both sides},\\ \boxed{\mathbf{y=8}} $$

**Therefore, the numbers are 10 and 8.**

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from High School Algebra II: Help and Review

Chapter 7 / Lesson 9