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Ordered triple

from class:

Algebra and Trigonometry

Definition

An ordered triple is a set of three numbers $(x, y, z)$ that represent a point in three-dimensional space. It is used to denote solutions to systems of linear equations involving three variables.

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5 Must Know Facts For Your Next Test

  1. Ordered triples are used to represent points in 3D coordinate systems.
  2. A solution to a system of linear equations with three variables can be expressed as an ordered triple $(x, y, z)$.
  3. Graphically, an ordered triple can be visualized as the intersection point of three planes in space.
  4. Each component of an ordered triple corresponds to a specific axis: $x$, $y$, and $z$ respectively.
  5. Inconsistent systems involving three variables will not have a common ordered triple solution.

Review Questions

  • What does the ordered triple $(x, y, z)$ represent in a system of linear equations?
  • How can you interpret the graphical representation of an ordered triple?
  • What happens if a system with three variables has no solution?

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