Ordered triple

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.

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?

Related terms

System of Linear Equations: A collection of two or more linear equations involving the same set of variables.

Three-Dimensional Coordinate System: A geometric setting in which each point is described by an ordered triple $(x, y, z)$. It consists of three mutually perpendicular axes: $x$, $y$, and $z$.

Intersection Point: The point where two or more geometric figures meet. In the context of linear equations, it represents the common solution.