Consistent system

Definition

A consistent system is a set of equations that has at least one solution. In a system of linear equations with two variables, this means the lines intersect at one or more points.

5 Must Know Facts For Your Next Test

1. A consistent system can be either independent or dependent.
2. An independent consistent system has exactly one solution where the lines intersect.
3. A dependent consistent system has infinitely many solutions because the lines are coincident (i.e., they lie on top of each other).
4. Graphically, an independent consistent system shows two lines intersecting at a single point.
5. Algebraically, consistency can be determined using methods such as substitution, elimination, or matrix operations.

Review Questions

• What characterizes a consistent system in terms of its solutions?
• How can you identify a dependent consistent system graphically?
• Which methods can be used to solve for the solutions of a consistent system?

Related terms

Independent System: A type of consistent system that has exactly one solution where two lines intersect.

Dependent System: A type of consistent system that has infinitely many solutions because the equations represent the same line.

Inconsistent System: A set of equations that has no solutions; graphically represented by parallel lines that never intersect.