General behavior

The solution set for two equations in three variables is usually a line.

The solution set for two equations in three variables is usually a line.

In general, the behavior of a linear system is determined by the relationship between the number of equations and the number of unknowns:

1. Usually, a system with fewer equations than unknowns has infinitely many solutions.

2. Usually, a system with the same number of equations and unknowns has a single unique solution.

3. Usually, a system with more equations than unknowns has no solution.