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Chapter 6.6
Solving 3 variable systems of equations (no solution, infinite solutions)
What You'll Learn
Recognize when a 3-variable system has no solution by identifying contradictions
Identify infinite solutions when equations are multiples of each other
Apply elimination methods to pairs of equations in a 3-variable system
Interpret geometric meaning: overlapping planes yield infinite solutions, parallel planes yield none
Verify solution types by analyzing the result after variable elimination
What You'll Practice
1
Solving systems that result in false statements like 0 = 20
2
Identifying equations that are multiples of each other
3
Using multiplication and elimination on equation pairs
4
Determining whether a system has no solution or infinite solutions
Why This Matters
Understanding no solution and infinite solution cases is crucial for recognizing when systems are inconsistent or dependent. This skill helps you avoid wasting time on unsolvable problems and prepares you for linear algebra, where analyzing solution types is fundamental.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Skills
Systems of Equations
Three Variables
Elimination Method
No Solution
Infinite Solutions
Dependent Equations
Inconsistent Systems
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