Systems of Equations involving Three Variables

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Examples, videos, worksheets, solutions, and activities to help Algebra students learn how to solve systems of equations involving three variables.

Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 1
2x - y + z = 3
5x + 2y - 3z = 1
2x + y - z = 2 Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 2
x + 2y + z = 12
2x - 2y - z = 6
x + 2y - z = 2

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Solving a System of Equations Involving 3 Variables
Using Elimination by Addition - Example 3
4x - 4y + 8z = 20
8x + 4y - 4z = 4
12x - 8y - 12z = -40 Solving a Dependent System of Linear Equations involving 3 Variables
Dependent systems have infinitely many solutions.
Solve. If the system is dependent, let z = c and write the solutions in terms of c.
x + 2y + z = 0
3x + 2y -z = 4
-x + 2y + 3z = -4

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