## systems_graphically_functions.docx - Section 2: Investigation

*systems_graphically_functions.docx*

# How are Systems of Equations related to Equations and Functions?

Lesson 6 of 13

## Objective: Students will understand how a linear equation can be represented as a system of equations graphically. They will be able to write an equation as a system and solve it both algebraically and graphically showing that both solutions are the same.

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#### Investigation

*15 min*

In questions #1-3, students will make connections with solving a system of equations algebraically and solving the system graphically. This serves as an introduction to the substitution method of solving a system of equations. Students are able to connect a procedure that they have mastered in 7th and 8th grade to the concept of functions. Students can also verify that the procedure extends to other functions such as absolute value and exponential functions. Solving abosolute value and exponential functions algebraically is not required but can be used as an extension.

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#### Closure

*15 min*

Writing prompt: If someone from our class was absent today, how would you explain the lesson? What things did you find confusing that you might want to emphasize? What things were easy?

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- LESSON 1: Introduction to systems of equations
- LESSON 2: What Does a System of Equations Really Look Like?
- LESSON 3: What is the "Point" of Solving a System?
- LESSON 4: Fitness Center Question
- LESSON 5: Cell Phone Plans
- LESSON 6: How are Systems of Equations related to Equations and Functions?
- LESSON 7: Solving Systems of Equations Without a Graph
- LESSON 8: Practice with the Substitution Method
- LESSON 9: Penny Problem
- LESSON 10: Practice Solving Systems Algebraically
- LESSON 11: Pulling the Systems Concepts All Together
- LESSON 12: An Interesting Lottery
- LESSON 13: Don't Sink The Boat