# Lesson Plan: Solving Systems of Linear Equations Graphically Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve a system of two linear equations by considering their graphs and identifying the point of intersection.

#### Objectives

Students will be able to

• understand that the solution set to a system of equations is graphically represented by the point or points at which the lines intersect,
• understand the possible solution cases when solving a system of linear equations:
• 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,
• an inconsistent system of linear equations (parallel lines) has no solutions,
• identify how many solutions a system of linear equations has when given the graph of the system,
• find the solutions to a system of linear equations when given the graph of the system:
• the graph and the two equations,
• the graph only,
• the two equations only (by constructing a graph),
• find the appropriate range or ranges for solutions to a system of linear equations when solving graphically.

#### Prerequisites

Students should already be familiar with

• equations involving two variables,
• the equation of a straight line in slope–intercept form,
• graphing linear functions.

#### Exclusions

Students will not cover

• systems of equations involving more than 2 variables,
• solving systems of equations algebraically.