Difference between revisions of "Systems of Equations in Three Variables"

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==Resources==
 
==Resources==
 
* [https://tutorial.math.lamar.edu/classes/alg/systemsthreevrble.aspx Linear Systems with Three Variables], Paul's Online Notes (Lamar Math)
 
* [https://tutorial.math.lamar.edu/classes/alg/systemsthreevrble.aspx Linear Systems with Three Variables], Paul's Online Notes (Lamar Math)
 +
* [https://courses.lumenlearning.com/wmopen-collegealgebra/chapter/introduction-systems-of-linear-equations-three-variables/ Systems of Equations: Three Variables], Lumen Learning
 +
* [https://www.youtube.com/watch?v=CdpFu7t0dJ4 Using Elimination to Solve a 3-Variable System], patrickJMT
 +
* [https://www.youtube.com/watch?v=tGPSEXVYw_o Solving a System of Two Equations with Three Variables (Infinite Solutions)], patrickJMT

Revision as of 11:01, 15 September 2021

See Systems of Equations in Two Variables for more information on systems of equations.

Examples

  • One solution: , , and . . We can add this to the third equation to get , which means z = 1. So, the first two equations can be rewritten as and . Using substitution, elimination, or graphing, we can calculate that x = 1 and y = 1 with these two equations. Thus, the solution to the system is (x, y, z) = (1, 1, 1).
  • No solutions: , , . These equations represent three parallel planes, and there is no x, y, and z that satisfy all three equations simultaneously. So, this system has no solutions.
  • Infinite solutions: , , . x + y = 0 for all x and y such that y = -x. Since when z = 0, this system has an infinite number of solutions of the form (x, -x, 0) where x can be any real number (for example, and are solutions of this system of equations).

Resources