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Solving Linear Equations:

Elimination and substitution

Justin P. Smithson

UW-La Crosse, Integrated Tech

April 28, 2015

Table of Contents

Dedication................................................1

Cover Page...............................................2

Table of Contents.....................................3

Cover........................................................4

Captain Jack and Cindy.........................5-6

Objective..................................................7

Define Variables.......................................8

Elimination and Substitution..............9-13

Conclusion..............................................14

References..............................................15

STORY TIME

Captain Jack is picking oranges and apples. At the 

end of the day, Jack has picked 4 oranges and 5 

apples that cost $3.56.

Captain Jack's friend, Cindy: The Beautiful 

CaveWomen, bought 3 apples and 4 oranges for the 

price of $2.76.

Our goal: To find the cost of an 

orange and the cost of an 

apple.

       =$?

       =$?

First: we need to define our variables: 

Let the number of oranges be x and the 

number of apples be y. Therefore, we 

can set up the following equations:

4x+5y=$3.56

3x+4y=$2.76

Recall: We learned how to solve a 

system of linear equations two ways:

1. Elimination;

2. Substitution

Ultimately, we can solve this using 

either method...let us do both ways for 

practice! 

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