Algebra I: How Many Solutions to the System?

Objectives

• Students will understand that a system of two linear equations in two variables can have one solution, no solution, or infinitely many solutions.
• Students will understand the connection between the slopes of the lines and the number of solutions to a system of linear equations in two variables.

Vocabulary

• system of two linear equations
• solution

About the Lesson

This lesson involves graphing systems of linear equations. The emphasis is on helping students understand the difference between systems that have one, infinitely many, or no solutions. As a result, students will:

• Manipulate a movable line in the coordinate plane in relation to a fixed line to satisfy certain conditions.
• Observe the slope and y-intercept changing as they manipulate the line.
• Discover what must be true for a system of equations to have one, infinitely many, or no solutions.