# If a system of equations has linearly dependent equations and an equal number of equations and variables, does it have to be consistent?

##### 1 Answer

No.

#### Explanation:

A linearly dependent system with an equal number of equations and unknowns is not necessarily consistent or inconsistent. It can be one or the other, depending upon the specific system. This is best proved by example.

Consider the system:

The system is dependent because the second equation can be reduced to

Consider the system:

This is a system with three equations and three unknowns. It is dependent because equation 2 is a constant multiple of equation 1. Additionally, it is inconsistent, because clearly

We have seen two examples of a linearly dependent system with