## Examples for Solving a System of Equations using Technology.pdf - Section 3: Solve a system of equations with a non-linear function

*Examples for Solving a System of Equations using Technology.pdf*

# Use The TI-Nspire CX To Solve a System of Equations

Lesson 12 of 14

## Objective: SWBAT use the TI-Nspire Cx to solve a linear equation and apply the same calculator method to solve a system of linear equations.

In this lesson, I first introduce how to solve a complex linear equation in one variable by analyzing it as a system of equations. I teach my students to rewrite the original equation as two different equations, each a linear function in two variables. Then, my students use the TI-Nspire CX to solve the equation by finding the x-coordinate of the intersection point of the 2 lines. My goal is to prepare the students to use the same calculator procedure to solve a system of equations, and then a system with a non-linear function in the 3rd section.

Once I teach this procedure, I show the students how to apply the same procedure to different types of problems. I work Example 1 and Example 2 from the Examples I have planned. Then, I ask students to complete Problems 1, 2, and 3 on the Practice worksheet.

As students work, I walk around the classroom to assist struggling students and peers assist others as well. Several students are leaders in class when using technology. I allow them to help students who are slower at learning the calculator. I demonstrate Example 1 in the video below.

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After students complete Practice Problems 1, 2, and 3, I teach Example 3 and Example 4 from the Examples I have planned. I repeat the same procedure as in Section 1. I remind students that equations must be in y= form in order to enter them into the calculator. So, in Example 4 I review how to undo the equation and solve for y. Students are expected to follow along during the examples and practice the calculator steps as well when I am teaching.

Next, I ask students to complete Practice Problems 3 and 4 from the Practice Worksheet, again as guided practice, with me assisting students, as well as students assisting peers.

During this section, I also discuss the following questions with students:

- What would 2 equations look like if the 2 lines are parallel?
- How many points do parallel lines share?
- What is the solution to parallel lines?
- What do two equations that are the same line look like?
- How many points are on the same line?
- What is the solution to one line?

I demonstrate Example 4 in the video below:

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I present the last example to students, showing them a system of equations with one non-linear equation and a linear equation. I model for students how to find the two intersections when the line intersects with the parabola. I have not taught my quadratic unit yet, but I have introduced students to the tables of quadratics when comparing to linear and exponential functions, and images of each type of graph. Though students are not that familiar with the quadratic function, I demonstrate that the same calculator method to solve a system of linear equations, may be used for a system of equations with a non-linear equation.

I work Example 5 from the Examples I have planned in the video below:

After the video, students complete practice problem Number 6 on the Practice Worksheet and I have students hand in the worksheet to check the solution as a formative assessment. Students will be expected to be able to solve a system of equations with or without technology after this lesson. If students have the wrong solution on Number 6 of the Practice worksheet when I assess it, students will be allowed to replace the grade by working another system of equations on the calculator with a non-linear function.

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to a System of Linear Equations
- LESSON 2: The Best of 2 Cell Phone Plans
- LESSON 3: Who is 1st in the Father Daughter Race?
- LESSON 4: Can You Save The Diver in 7 Minutes?
- LESSON 5: Make a Substitution
- LESSON 6: Alternate Method to Solve a System of Equations by Substitution
- LESSON 7: Quarters, Dimes and Linear Combinations
- LESSON 8: Define, Set, Go!
- LESSON 9: Khan Your Way Into Solving a System of Equations Using Elimination
- LESSON 10: Elimination with 2 Column Notes
- LESSON 11: Assessment of a System of Linear Equations
- LESSON 12: Use The TI-Nspire CX To Solve a System of Equations
- LESSON 13: Solving a System of Inequalities
- LESSON 14: Solve the System of Inequalities to Find The Treasure!