# How many kinds of solutions are there?

##### 1 Answer

From the category in which this question is asked, I will assume you mean a finite linear system of equations. If such a system is in

#### Explanation:

If a linear system involves

(0) The empty set. The system is inconsistent and has no solutions.

(1) A unique solution in the form of an

(2) A line of solutions expressible as:

...

for all

(3) A plane of solutions expressible as:

...

for all

...

(n+1) The whole of