In a previous lesson, students learned that the solutions to a system of linear inequalities can be represented graphically with overlapping regions.
In this lesson, students take a closer look at whether points on the boundary lines of the system's solution region are included in the solutions. Analyzing graphs and communicating observations about them require attention to precision (MP6). Students also apply these insights to solve more challenging contextual problems. This work involves making sense of the information needed to solve the problems (MP1).
Lesson overview
 25.1 Warmup: Which One Doesn’t Belong: Graphs of Solutions (5 minutes)

25.2 Activity: Focusing on the Details (10 minutes)
 Includes "Are you Ready for More?" extension problem
 25.3 Activity: Info Gap: Terms of A Team (20 minutes)
 Lesson Synthesis
 25.4 Cooldown: Widgets and Zurls (5 minutes)
Learning goals:
 Analyze given information about a situation involving multiple constraints and determine what additional information is needed to solve problems.
 Given a system of inequalities and their graphs, explain (orally and in writing) how to tell if a pair of values is a solution to the system.
 Practice writing systems of inequalities in two variables and finding the solution sets by reasoning or by graphing.
Learning goals (student facing):
 Let’s use systems of inequalities to solve some problems.
Learning targets (student facing):
 I can explain how to tell if a point on the boundary of the graph of the solutions to a system of inequalities is a solution or not.
Required materials:
 Preprinted slips, cut from copies of the blackline master
Standards:
 This lesson builds towards the standard: CCSS.HSAREI.D.12MS.AREI.12MO.A1.REI.C.7MO.A1.REI.C.8
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.