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

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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.

Big Idea

Graphing technology is used to reinforce understanding of concepts and methods for solving systems of equations

Solve one linear equation with one variable

10 minutes

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.

 

 

Solve 2 equations with 2 variables

20 minutes

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:

 

 

 

Solve a system of equations with a non-linear function

20 minutes

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.