Algebra 57 - Dependent Equations and Systems

Some systems of linear equations contain one or more equations which don't add any new information to the system and are therefore redundant. These equations are said to be 'dependent'. In a system of two equations, it is easy to spot when the equations are dependent since the equations will be either identical or multiples of each other. In this case, the system will always have infinitely many solutions. However, in systems of more than two equations, dependent equations are not necessarily multiples of each other and the system may or may not have infinitely many solutions.