Consistent vs. Inconsistent Systems

A system of equations is a collection of equations in the same variables. For example, the following is a system of equations with variables x and y:

2x + 3y = -10
x – 3y = 4

Systems of equations can be subdivided into consistent or inconsistent systems.

A consistent system has at least one solution. If a system has exactly one solution, it is called independent. If a system has infinitely many solutions, it is called dependent. If a system does not have a solution, it is called inconsistent. As you work through solving systems of equations, you will be able to classify the system as either consistent or inconsistent. If the system is consistent, you will also be able to classify it as dependent or independent.