Solution of a linear equation
Definition: A solution of a linear equation like is any ordered list of numbers that makes the above equation true when we replace by , respectively .
Example: is a solution of the equation
Observe that a linear equation on two variables or more have infinite solutions.
Solution of a Linear system
Definition: Solution of a linear system is any ordered list that is a solution of all equations in the linear system.
Example: The list (or the point) is a solution of the following linear system on two variables
Number of solutions
A linear system has
- No solution, or
- Exactly one solution, or
- Infinitely many solutions.
Question: Why couldn’t there be only two (or three, or four, …) solutions?