Unit 7, Lesson 7
Solutions to Systems of Linear Inequalities in Two Variables
Integrated Math 1
Preparation
Lesson Narrative
In this lesson, students build on their understanding of linear inequalities in two variables to find the solutions to systems of linear inequalities in two variables.
Students learn that two linear inequalities that represent the constraints in the same situation form a system of inequalities, and that the solutions to the system include all numbers that satisfy both constraints simultaneously. Graphically, the solution set of the system is represented by the region where the graphs of the individual inequalities overlap.
Throughout the lesson, students endeavor to find values that satisfy multiple constraints, both in terms of a situation and in the absence of one. The process requires that students make sense of problems and persevere in solving them (MP1) and that students reason quantitatively and abstractly (MP2).
- Given descriptions and graphs that represent two constraints, identify values that satisfy each constraint and those that satisfy both constraints simultaneously.
- Understand that the solution set of a system of inequalities in two variables is composed of any pair of values that make both inequalities true, and that it is represented graphically by the region where the graphs overlap.
- Write systems of inequalities in two variables, use technology to graph the solutions, and interpret the solutions in context.