# 12. Solve systems by inspection (FP)

teaches Common Core State Standards CCSS.Math.Content.8.EE.C.8b http://corestandards.org/Math/Content/8/EE/C/8/b
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Solve systems by inspection, indicating the number of solutions.

This lesson helps to build fluency with finding the number of solutions without solving or graphing. Tables, graphs, and equations are used here because recognizing the same features in all three representations will help support students as they use different methods to solve. This work develops students' understanding that the slope and y-intercept can help to determine the number of solutions to a system.

Students engage in Mathematical Practice 8 (Look for and express regularity in repeated reasoning) as they analyze tables, graphs, and equations to determine the number of solutions based on the slope and y-intercept.

Key vocabulary:

• infinitely many solutions
• no solutions
• one solution
• slope
• y-intercept

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