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
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:
Skills You Will Master
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