# Two Worlds Collide, Part 2

## Systems of Linear Equations: Substitution and Elimination

Brittany VanCleave, Bj Sneed, Teresa Lansford, Michell Eike | Published: July 13th, 2022 by K20 Center

• Grade Level 9th, 10th, 11th
• Subject Mathematics
• Course Algebra 1, Algebra 2
• Time Frame 115-150 minutes
• Duration 2-3 class periods

### Summary

This lesson focuses on how to analyze and solve systems of linear equations by using the substitution and elimination methods. Students will use their prior knowledge of the components of a system to solve problems algebraically. Students will identify, solve, and write equations using substitution and/or elimination as their tools. This is the second lesson of three in the "Two Worlds Collide" lesson series.

### Essential Question(s)

How can systems of equations be used to represent situations and solve problems?

### Snapshot

Engage

Students use the Tell Me Everything strategy to activate prior knowledge.

Explore

Students investigate different algebraic methods through a Desmos "Line Zapper" activity.

Explain

Students discuss their findings from the Desmos activity and formalize their understanding of the substitution and elimination methods.

Extend

Students expand their knowledge through a second Desmos activity, "Wafers and Crème," based on a real-world scenario.

Evaluate

Students determine which method works best to solve a given problem and share their reasoning. Students reflect on their confidence in using the two algebraic methods.

### Materials

• Lesson Slides (attached)

• Note Catcher handout (attached; one per student; printed front/back)

• Which Method handout (attached; one per student; printed front only)

• Paper

• Pencil

• Laptop or tablet with internet access

### Engage

5 Minute(s)

Introduce the lesson using the attached Lesson Slides. Display slide 3 to share the lesson's essential question. Display slide 4 to go over the lesson's learning objectives. Review these slides with students to the extent you feel necessary.

Assign student pairs or have each student find a partner. Go to slide 5 and pass out the attached Note Catcher handout to each student.

On the top portion of the handout, have students use the Tell Me Everything strategy to write everything they know about the words substitution and elimination. Encourage students to write or draw anything that comes to mind, whether it’s a definition, an example, a picture, or something else.

Once students have written or drawn something for both words, give students time to discuss in pairs. Then, invite several pairs to share out. Keep in mind this portion of the lesson is just meant to activate students’ prior knowledge and get them thinking about the concepts.

### Explore

30 Minute(s)

Display slide 6 and provide students with your session code. Then, have students go to student.desmos.com and enter the session code.

During the activity, students go through nine screens and work in pairs to "zap" different points of intersection based on the equation and/or graph provided. Have students use the Desmos: Line Zapper portion of the Note Catcher (and additional scratch paper, if needed) as a space to investigate the equations and write down their thoughts as they work.

The activity does not specifically tell students how to solve the equations, so they may use any algebraic method they want. This is a time for students to explore their knowledge, figure out a process that works best for them, and reflect with their partners.

### Explain

25 Minute(s)

Have each student pair join another pair to form a group of four or assign groups of four. Display slide 7. In groups, have students unpack the Desmos activity by discussing the following questions:

• How can you determine the exact solution to a system of equations?

• What did you feel was the hardest part of the activity?

• What became easier as you progressed through the activity?

Ask for volunteers to share their responses with the whole class.

Go to slide 8. Inform students they are going to use the 3-2-1 strategy to complete the Substitution: 3-2-1 portion of the Note Catcher as they watch the following video.

Go to slide 9 and play Khan Academy’s video, "The Substitution Method," which demonstrates how to solve systems of equations with the substitution method:

After the video, go to slide 10 and ask for volunteers to share their answers to the questions on the handout:

• What are three things you learned?

• What are two questions you still have?

• What is one thing you found interesting?

Depending on students’ questions and feedback, you may have to solve another problem using substitution as a class until all misconceptions are cleared up. This may vary from class to class.

Repeat the same process for the elimination method by transitioning through slides 11–13. Have students complete the Elimination: 3-2-1 portion of the Note Catcher as they watch Khan Academy’s video, "Solving Systems With Elimination":

Depending on students’ questions and feedback, you may have to solve another problem using elimination as a class until all misconceptions are cleared up. This may vary from class to class.

### Extend

30 Minute(s)

Display slide 14. Provide students with your session code. Then, have students go to student.desmos.com and enter the session code.

During the activity, students apply their knowledge of substitution and/or elimination to a real-world scenario to determine the number of calories in a pack of triple-crème cookies. Have students use the Desmos: Wafers and Crème portion of the Note Catcher (and additional scratch paper, if needed) as a space to solve the system of equations.

To help students check their expressions, prompt them to use the sliders to adjust the number of cookies and layers of crème to recreate the cookie packs shown on previous screens. When a student selects six cookies with single crème filling, for example, the screen will show the number of calories their expression would yield—which should be 320 calories if their expression is correct.

Have students recreate all three packs of cookies to check their work.

### Evaluate

10 Minute(s)

Go to slide 15 and pass out the attached Which Method handout to each student.

For each problem, ask students to decide if they should use substitution or elimination to solve it. Have students write their thoughts on the handout. Remind students that, while both methods always work, one method may be easier to use on certain problems.

Students continue to apply what they have learned in this series’ final lesson: "Two Worlds Collide, Part 3."

### Resources

Desmos Classroom. (n.d.). Line Zapper [Interactive activity]. Desmos. https://teacher.desmos.com/activitybuilder/custom/5df166d1fa83ee79c328d37d?collections=5da6485a83c0877d4b5708dd

Desmos Classroom. (n.d.). Wafers and Crème [Interactive activity]. Desmos. https://teacher.desmos.com/activitybuilder/custom/56d74abe3df0d04006f0cb97?collections=5da6485a83c0877d4b5708dd