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?

Addition Method:

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.

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 -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}

Adding (1) and (2):

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

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}.


Learn more about this topic:

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Elimination Method in Algebra: Definition & Examples

from High School Algebra II: Help and Review

Chapter 7 / Lesson 9
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