# Lesson 26

Modeling with Systems of Inequalities in Two Variables

### Lesson Narrative

In this culminating lesson, students integrate the ideas from the unit and engage in multiple aspects of mathematical modeling (MP4).

In the first activity, they interpret and analyze given models that represent the constraints and conditions in a situation. In the second activity, they create their own models after specifying quantities of interest, identifying relevant information, and setting the constraints.

### Learning Goals

Teacher Facing

• Define the constraints in a situation and create a mathematical model to represent them.
• Interpret a mathematical model, presented as inequalities and graphs, that represents a situation.

### Student Facing

• Let’s create mathematical models using systems of inequalities.

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)

### Student Facing

• I can interpret inequalities and graphs in a mathematical model.
• I know how to choose variables, specify the constraints, and write inequalities to create a mathematical model.

### 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.

### Print Formatted Materials

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