Unit 5 — Systems of Inequalities

Unit 5 · Systems of Inequalities

Systems of Inequalities

Graph and solve systems of linear inequalities. Identify feasible regions, interpret solutions in context, and apply systems of inequalities to real-world optimization problems.

Estimated Time

30–40 minutes

Difficulty

Intermediate

6 Lessons
6 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 5 — Systems of Inequalities extends your work with systems of equations into the world of inequalities. Instead of finding a single point of intersection, you will identify entire regions of the coordinate plane that satisfy multiple constraints simultaneously — a powerful tool for real-world optimization.

Learning Objectives

By the end of this unit, you will be able to:

Goal 1Graph a single linear inequality on the coordinate plane and identify the solution region.
Goal 2Graph a system of two or more linear inequalities and identify the feasible region.
Goal 3Determine whether a given ordered pair is a solution to a system of inequalities.
Goal 4Write a system of inequalities from a graph or real-world description.
Goal 5Identify systems with no solution (empty feasible region) and unbounded solution regions.
Goal 6Apply systems of inequalities to real-world problems involving constraints and optimization.

Skills You Will Master

Graphing inequalities
Identifying solution regions
Verifying solutions
Writing systems from context
Special cases (no solution)
Real-world applications

Real-World Connection

Systems of inequalities model real-world constraints every day. A business owner uses them to determine how many products to make given limited resources. A nutritionist uses them to design meal plans that meet minimum nutritional requirements without exceeding calorie limits. City planners use them to zone land use. In linear programming — used in logistics, manufacturing, and finance — systems of inequalities define the feasible region within which the optimal solution must lie. Mastering this unit gives you a direct path into applied mathematics and operations research.

Chapter Checklist

Recommended steps for completing each chapter

  • Read the Workbook
  • Complete the Independent Study
  • Finish the Exit Ticket
  • Take the Quiz
  • Review the Answer Key
  • Continue to the Next Chapter