key term - Consistent system

Definition

A consistent system is a set of equations that has at least one solution. In a graph, the lines representing the equations intersect at one or more points.

5 Must Know Facts For Your Next Test

1. In a consistent system with two linear equations, the lines intersect at exactly one point or overlap completely.
2. Consistent systems can be either independent (one unique solution) or dependent (infinitely many solutions).
3. Graphically, a consistent and independent system shows two lines crossing at a single point.
4. For a consistent and dependent system, the equations represent the same line.
5. If solving algebraically, consistent systems yield a true statement like $x = x$ or specific values for variables.

Review Questions

Related terms

Inconsistent System:

A set of equations with no solutions; graphically represented by parallel lines that never intersect.

Independent System: A consistent system where there is exactly one unique solution; graphically represented by intersecting lines at exactly one point.

Dependent System:

A consistent system where there are infinitely many solutions; graphically represented by coinciding lines.