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Unit 4 - Lesson 13 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 4
Lesson 13: Solving Systems of Equations
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 4
Lesson 13: Solving Systems of Equations
CC BY 2021 Illustrative Mathematics®
Lesson: Solving Systems of Equations

True or False: Two Lines (Warm Up)

Use the lines to decide whether each statement is true or false. Be prepared to explain your reasoning using the lines.
1.

A solution to 8 = -x + 10 is 2.

2.

Explain your reasoning using the lines.

3.

A solution to 2 = 2x + 4 is 8.

4.

Explain your reasoning using the lines.

5.

A solution to -x + 10 = 2x + 4 is 8.

6.

Explain your reasoning using the lines.

7.

A solution to -x + 10 = 2x + 4 is 2.

8.

Explain your reasoning using the lines.

9.

There are no values of x and y that make y = -x + 10 and y = 2x + 4 true at the same time.

10.

Explain your reasoning using the lines.

Matching Graphs to Systems

Here are three systems of equations graphed on a coordinate plane:

Match each figure to one of the systems of equations shown here.
11.

12.

13.

14.

Find the solution to each system and check that your solution is reasonable based on the graph.


Different Types of Systems

Your teacher will give you a page with some systems of equations. Graph each system of equations carefully on the provided coordinate plane.
15.

System of equations #1

16.

System of equations #2

17.

System of equations #3

18.

System of equations #4

Describe what the graph of a system of equations looks like when it has . . .
19.

1 solution

20.

0 solutions

21.

Infinitely many solutions

Cool Down

Two Lines

22.

Given the lines shown here, what are two possible equations for this system of equations?


23.

How many solutions does this system of equations have? Explain your reasoning.