More Lessons for Grade 11 Math

Math Worksheets

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

Systems of Three Variables

Solve this system

x + y - 3z = -10

x - y + 2z = 3

2x + y - z = -6

Solve the system

x + 2y + 5z = -17

2x - 3y + 2z = -16

3x + y - z = 3

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.

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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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.