In linear algebra, what is the difference between a consistent and inconsistent system?

Answer 1

The difference is whether or not the lines of the equations intersect. Recall in Algebra, when these lines do intersect, the X and Y pair at the intersection is the point on the graph where the same solution is true for both equations. When this occurs, the system is called consistent.

In contract, if the lines representing the equations are parallel, they will never intersect and they will never have a shared X and Y point that makes them true at the same time. This system is said to be inconsistent.