Linear Systems in 3 Variables Worksheets

Printable “Systems of Equations” worksheets:
Solve Systems of Equations with Substitution
Solve Systems of Equations with Elimination
Solve Systems of Equation Word Problems
System of Equations using the Graphical Method
System of Equations Word Problems using the Graphical Method
System of Equations with No Solution
System of Equations with 3 Variables
Intersection of Circles & Lines

Examples, solutions, videos, and worksheets to help Algebra II students learn how to solve linear systems in three variables algebraically using substitution or elimination.

How to Solve Linear Systems of Three Variables?

A system of three linear equations involves three variables. The goal is to find values for all three variables that satisfy all the equations simultaneously. There are two main methods to solve such systems: substitution, and elimination.

Steps for Solving a System of Three Variables
Method 1: Substitution

1. Choose one equation to solve for one variable in terms of the others (e.g., solve for 𝑥 in terms of 𝑦 and 𝑧).
2. Substitute the expression for that variable into the other two equations. This reduces the system to two equations with two variables.
3. Solve the resulting two-variable system using substitution or elimination.
4. Back-substitute the found values into one of the original equations to find the third variable.

Method 2: Elimination

1. Eliminate one variable by combining two equations to cancel it out.
   Multiply equations by appropriate values so that adding or subtracting them eliminates one variable.
2. Repeat the elimination process for another pair of equations to create a new system with two variables.
3. Solve the resulting two-variable system.
4. Back-substitute to find the third variable.

Have a look at this video if you need to review how to solve Linear Systems in 3 Variables.

• Solving Systems of 3 Equations (Elimination)

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More Linear Systems of Three Variables Worksheets

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(Answers on the second page.)
Linear Systems in 3 Variables Worksheet #1
Linear Systems in 3 Variables Worksheet #2

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Linear Systems in 3 Variables

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