Unit 4 — Systems of Equations

Unit 4 · Systems of Equations

Systems of Equations

Solve systems of two linear equations using graphing, substitution, and elimination. Interpret solutions as intersection points and apply systems to real-world problems.

Estimated Time

35–45 minutes

Difficulty

Intermediate

7 Lessons
6 Learning Goals
10 Vocabulary Terms

Overview

Unit description, learning objectives, and skills.

Unit 4 — Systems of Equations teaches you to solve two equations at once. You will use graphing, substitution, and elimination to find the point where two lines intersect, and apply systems to real-world problems involving mixtures, rates, and comparisons.

Learning Objectives

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

Goal 1Understand what a system of equations is and identify solutions as ordered pairs.
Goal 2Classify systems as having one solution, no solution, or infinitely many solutions.
Goal 3Solve systems of equations by graphing two lines and identifying the point of intersection.
Goal 4Solve systems algebraically using the substitution method.
Goal 5Solve systems algebraically using the elimination method.
Goal 6Write and solve systems of equations from real-world word problems.

Skills You Will Master

Solving by graphing
Substitution method
Elimination method
Classifying systems
Word problems
Checking solutions

Real-World Connection

Systems of equations model situations where two conditions must be true at the same time. A business owner who needs to know how many units to sell to break even is solving a system. A chemist mixing two solutions to hit a target concentration is solving a system. Even planning a road trip — balancing distance, speed, and time across two routes — uses the same logic. Mastering systems gives you the power to solve problems with multiple unknowns simultaneously, a skill used in economics, engineering, science, and everyday decision-making.

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