Module 5: Systems of Equations & Inequalities
Master solving systems using multiple methods and apply to real-world scenarios
Your Progress
Complete all lessons, practice, and assessments to earn your Module 5 badge!
0 of 12 items completed
Learning Objectives
By the end of this module, you will be able to:
- Solve systems of two linear equations using substitution, elimination, and graphing methods
- Identify whether a system has one solution, no solution, or infinitely many solutions
- Solve systems of three equations with three variables using elimination and matrices
- Use augmented matrices and row operations to solve systems efficiently
- Graph linear inequalities in two variables and identify solution regions
- Solve systems of linear inequalities and apply to linear programming problems
Lessons
Work through each lesson in order. Each lesson includes examples, interactive visualizations, and check-your-understanding questions.
Systems of Linear Equations
Solve systems by graphing, substitution, and elimination. Classify systems as consistent, inconsistent, or dependent, and apply to real-world problems.
Matrices and Systems of Equations
Represent systems as augmented matrices and use Gaussian and Gauss-Jordan elimination to solve them efficiently.
Nonlinear Systems
Solve systems where at least one equation is nonlinear using substitution and elimination, and interpret solutions both algebraically and graphically.
Inequalities and Linear Programming
Graph linear inequalities, find feasible regions, and apply the Corner Point Theorem to solve real-world optimization problems.
Assessments & Practice
Pre-Assessment
5 questions to gauge your starting knowledge
Not StartedPractice Problems
20 comprehensive problems with detailed solutions
Not StartedModule Quiz
15-question quiz (70% to pass)
Not StartedPost-Assessment
5 questions to measure your learning gains
Not StartedStudy Materials
Ready to Begin?
Start with the pre-assessment to see what you already know!