The sum of two numbers is 18 and their difference is 2. What are the numbers?

Question:

The sum of two numbers is 18 and their difference is 2. What are the numbers?

Elimination Method:

(i) The elimination method is used to solve a system of two equations in two variables.

(ii) In this method, we add or subtract the given equations and eliminate one variable.

(iii) We solve the resultant equation in one variable using the algebraic operations.

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 {eq}\boxed{\mathbf{10}} {/eq} and {eq}\boxed{\mathbf{8}} {/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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