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Given that the sum of two numbers is 20 and their difference is 6, find the two numbers.

Question:

Given that the sum of two numbers is 20 and their difference is 6, find the two 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 20. So we get: {eq}x+y=20 \,\,\,\rightarrow (1) {/eq}.

The difference between the two numbers is 6. So we get: {eq}x-y=6\,\,\,\rightarrow (2) {/eq}

Adding (1) and (2):

$$x+y+x-y =20 +6 \\ 2x = 26\\ \text{Dividing both sides by 2}, \\ \boxed{\mathbf{x=13}} $$

Substitute this in (1):

$$13+y=20\\ \text{Subtracting 13 from both sides},\\ \boxed{\mathbf{y=7}} $$

Therefore, the numbers are 13 and 7.


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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