# What are the two numbers if their sum is -7 and their difference is 14?

## Question:

What are the two numbers if their sum is -7 and their difference is 14?

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

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

The sum of the two numbers is -7. So we get: {eq}x+y=-7\,\,\,\rightarrow (1) {/eq}.

The difference between the two numbers is 14. So we get: {eq}x-y=14\,\,\,\rightarrow (2) {/eq}

$$x+y+x-y =-7+14 \\ 2x = 7\\ \text{Dividing both sides by 2}, \\ \boxed{\mathbf{x=3.5}}$$

Substitute this in (1):

$$3.5+y=-7\\ \text{Subtracting 3.5from both sides},\\ \boxed{\mathbf{y=-10.5}}$$

Therefore, the numbers are {eq}\boxed{\mathbf{3.5}} {/eq} and {eq}\boxed{\mathbf{-10.5}} {/eq}.