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Overview
Foundations of Mathematics and Pre-Calculus 10
6. Systems of linear equations
6.8 Solving 3 variable systems of equations by elimination
Solving 3 Variable Systems of Equations by Elimination
Master the elimination method for 3 variable systems of equations: combine equations in pairs to knock out variables and solve for x, y, and z.
What You'll Learn
Identify a 3 variable system as three linear equations that share the unknowns x, y, and z.
Apply the elimination method by adding or subtracting pairs of equations to cancel one variable at a time.
Reduce the 3 variable system to a 2 variable system once one unknown has been eliminated.
Solve the resulting 2 variable system using elimination or substitution to find two of the unknowns.
Back-substitute the known values into an original equation to find the third variable.
Check every solution in all three original equations to confirm the answer is correct.
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
Learning resources
Skills
Elimination Method
Systems of Equations
Three Variables
Algebraic Manipulation
Back-Substitution
Linear Systems
BC Curriculum Aligned