# Systems of 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.

Systems of Three Variables
Example:
Solve this system
x + y - 3z = -10
x - y + 2z = 3
2x + y - z = -6
Systems of Three Variables 2
Solve the system
x + 2y + 5z = -17
2x - 3y + 2z = -16
3x + y - z = 3

Three Equation Application Problem
Solve the following application problem using three equations with three unknowns.
Example:
The second angle of a triangle is 50 degrees less than 4 times the first angle. The third angle is 40 degrees less than th first. Find the measures of the three angles.
Solutions to Three Variable System
Example:
Determine whether this system has no solutions or infinite solutions
2x - 4y + z = 3
8x - 2y + 4z =7
-4x + y - 2z = -14

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