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6-8 Grade 8 Unit 3 Lesson 13

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Lesson 13

13.1 Warm-up 13.2 Activity 13.3 Activity Student Lesson Summary Glossary

Unit 3, Lesson 13

Solutions to Linear Equations

Grade 8

13.1

Warm-up

Avocados and Pineapples

At the market, avocados cost $1 each and pineapples cost $2 each. Find the cost of:

6 avocados and 3 pineapples
4 avocados and 4 pineapples
5 avocados and 4 pineapples
8 avocados and 2 pineapples

Are You Ready for More?

13.2

Activity

More Avocados and Pineapples

At the market, avocados cost $1 each and pineapples cost $2 each.

Noah has $10 to spend at the produce market. Can he buy 7 avocados and 2 pineapples? Explain or show your reasoning.
What combinations of avocados and pineapples can Noah buy if he spends all of his $10?
Write an equation that represents $10 combinations of avocados and pineapples, using for the number of avocados and for the number of pineapples.
What are 3 combinations of avocados and pineapples that make your equation true? What are three combinations of avocados and pineapples that make it false?

Are You Ready for More?

13.3

Activity

Solutions and Everything Else

There are two numbers. When the first number is doubled and added to the second number, the sum is 10.

Let represent the first number and let represent the second number. Write an equation showing the relationship between , , and 10.
Draw and label a coordinate plane.
Find 5 pairs of - and -values that make the statement and your equation true. Plot each pair of values as a point on the coordinate plane. What do you notice?
List 10 pairs of - and -values that do not make the statement and equation true. Using a different color, plot each pair of values as a point on the coordinate plane. What do you notice about these points compared to your first set of points?

Are You Ready for More?

Student Lesson Summary

A solution to an equation with two variables is any pair of values for the variables that make the equation true. For example, the equation represents the relationship between the width and length for rectangles with a perimeter of 8 units. One solution to the equation is that the width and length could be 1 and 3, since . Another solution is that the width and length could be 2.75 and 1.25, since . There are many other possible pairs of width and length that make the equation true.

The pairs of numbers that are solutions to an equation can be seen as points on the coordinate plane where every point represents a different rectangle whose perimeter is 8 units. Here is part of the line created by all the points that are solutions to . In this situation, it makes sense for the graph to only include positive values for and since there is no such thing as a rectangle with a negative side length.

Graph of a line, origin O, with grid.

Glossary

solution to an equation with two variables

A solution to an equation with 2 variables is a pair of values for the variables that make the equation true.

For example, one solution to the equation is . Substituting 6 for and 0 for makes this equation true because .