Lesson 25

Solving Problems with Systems of Linear Inequalities in Two Variables

Lesson Narrative

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).


Learning Goals

Teacher Facing

  • 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.

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.

CCSS Standards

Addressing

Building Towards

Glossary Entries

  • solutions to a system of inequalities

    All pairs of values that make the inequalities in a system true are solutions to the system. The solutions to a system of inequalities can be represented by the points in the region where the graphs of the two inequalities overlap.

  • system of inequalities

    Two or more inequalities that represent the constraints in the same situation form a system of inequalities.

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