There are three types of systems of linear equations.

• Lines are either consistent or inconsistent. If they are consistent, they have at least one solution or intersection. If they are inconsistent they have no solutions or intersections.
• Lines are also independent or dependent. If they are independent, they have exactly one solution; and if they are dependent, they have infinitely many solutions.

Intersecting lines are consistent and independent. They have exactly one solution.

Coinciding lines are consistent and dependent. They have an infinite number of solutions.

Parallel lines are inconsistent. They will never intersect and there are no solutions.