# Lesson Plan: Solution Cases of System of Linear Equations Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine whether a linear system of equations has a unique solution, no solution, or an infinite number of solutions.

#### Objectives

Students will be able to

- understand the possible solution cases when solving a system of linear equations, particularly that an independent system of linear equations (nonparallel lines) has one solution, a dependent system of linear equations (coincident lines) has an infinite number of solutions, and an inconsistent system of linear equations (parallel lines) has no solution,
- determine the number of solutions to a system of linear equations from a given graph of the system,
- understand the relationships between the slopes of the lines in a system of linear equations and the number of solutions,
- identify the number of solutions to a system of linear equations using their slopes and intercepts.

#### Prerequisites

Students should already be familiar with

- slopes of lines and graphing linear equations,
- the slope–intercept form.

#### Exclusions

Students will not cover

- explicitly solving a system of equations, graphically or otherwise,
- systems with more than two equations,
- systems in more than two variables.