# Solving Systems

Click on the image at right to get the lesson app with instructor notes. Or you can install right from here by clicking the logo below: Students are introduced to systems of (two) linear equations, Students explore systems with one solution and no solutions by building systems with certain solutions using an interactive graphing tool. They then identify systems with one solution, no solutions, or infinite solutions based on the slopes given by the equations. Throughout, equations are given in different forms and students are expected to rewrite in order to compare them.

In the second module, students are shown two approaches to solving systems of equations using algebra—elimination and substitution. Students solve a variety of different systems using these methods. In the Student notes, it is explained that a system with no solutions results in a false equation, such as 4 = 5. A system with infinite solutions results in an equation such as 5 = 5.

Finally, students solve systems of equations in a variety of different contexts. Students are provided the interactive graphing tool from Module 1 to model the system and check their work. Encourage students in this module to explain the meaning of the solution in terms of the context.

Module 1 Video

This video briefly introduces systems of equations and explains that they have either one, no, or infinite solutions. At the end of the video, students are encouraged to think of different examples for each system, and they are challenged to think of a context which can be modeled by each system.