Lesson Plan: Solving Systems of Linear Equations Graphically
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.
