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The sum of two numbers is 21 and their difference is 5, what are the two numbers?

Question:

The sum of two numbers is 21 and their difference is 5, what are the two numbers?

Elimination Method:

A system of two equations can be solved in many methods. One of the methods is the "elimination method". In this method, we add or subtract the equations to get a variable canceled. We will solve the resultant equation for the other variable.

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 21. So we get: {eq}x+y=21 \,\,\,\rightarrow (1) {/eq}.

The difference between the two numbers is 5. So we get: {eq}x-y=5\,\,\,\rightarrow (2) {/eq}

Adding (1) and (2):

$$x+y+x-y =21 +5 \\ 2x = 26\\ \text{Dividing both sides by 2}, \\ \boxed{\mathbf{x=13}} $$

Substitute this in (1):

$$13+y=21\\ \text{Subtracting 13 from both sides},\\ \boxed{\mathbf{y=8}} $$

Therefore, the numbers are 13 and 8.


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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