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Chapter 9.12
Solving 3 variable systems of equations by elimination
What You'll Learn
Apply elimination method to reduce 3-variable systems to 2-variable systems
Use strategic multiplication to create opposite coefficients for variable elimination
Solve pairs of equations systematically to isolate one variable at a time
Substitute solved values back into original equations to find remaining variables
Verify solutions by checking all three variables in the original system
What You'll Practice
1
Eliminating variables by adding equations with opposite coefficients
2
Multiplying entire equations to align coefficients before elimination
3
Solving reduced 2-variable systems to find individual variable values
4
Back-substituting to determine all three variables in order
Why This Matters
Mastering 3-variable systems prepares you for advanced algebra, linear algebra, and calculus. This skill is essential in physics, engineering, and economics where multiple equations model real-world situations like circuit analysis, optimization problems, and market equilibrium.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Skills
Elimination Method
Systems of Equations
Three Variables
Algebraic Manipulation
Back-Substitution
Linear Systems
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