# Activities

• • • ##### Subject Area

• Math: Algebra II: Systems of Linear Equations and Inequalities

• ##### Author 9-12

100 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS

## Solving Systems of Linear Equations from Four Perspectives

#### Activity Overview

Using the on-screen directions and the more detailed directions here, students will investigate four ways to solve systems of linear equations: graphically, numerically, with a data table and by matrices. Some prior familiarity with the basic functions of the TI-nspire CAS is needed. Students should be able to navigate between pages. Students should be able to use the menu functions on each screen.

#### Before the Activity

Load .tns file "equations" onto handhelds. Print copies of instructions for students or the lesson can be conducted as a teacher led activity. Most of the work is shown on the screen shots. These could be changed prior to loading on student handhelds if the activity is to be teacher led.

The matrix solution should be done after some explanation of reduced row echelon form is given in class.

This can be used as part of lessons over several days, teaching a traditional paper and pencil approach to systems of linear equations first and then following with the TI-nspire CAS. Any part of the calculator lesson can be used to introduce a system of linear equations.

For Algebra I level students, I would recommend using simpler equations where the intersection points are integers. The graphing approach is often the easiest for students to understand as an initial approach. Linear combination is done first here using a CAS version of the TI-nspire. Without a CAS system, graphing can come first.

This can serve as a review for Algebra 2 or Pre-Calculus students. The rref matrix solution is best used after students have some familiarity with matrices. An explanation of what the calculator does to solve a system of equations with matrices should precede the easy way to get an answer using rref.

#### During the Activity

The directions are included in the Word file and also in the .tns file.

Screen shots which show results are in the Word file.

#### After the Activity

An investigation of why the rref function works can be done using introductory Linear Algebra work. This is more appropriate for advanced Algebra 2 or Pre-Calculus students.