Types of Systems of Two Linear Equations in Two Variables
A system of linear equations in two variables may or may not have a solution.
If a system has a solution, then it is consistent. If it does not have a solution, then it is inconsistent.
If a system is consistent, it can be further classified as independent or dependent. An independent system has exactly one solution, while a dependent system has an infinite number of solutions.
The properties of each type of system of linear equations in two variables are given in the table below. Refer also to the figures after the table to see how the graph of each type of system looks like.
Types of Systems of Two Linear Equations in Two Variables
Sample Graphs of Systems of Two Linear Equations in Two Variables
a. consistent and independent system
b. consistent and dependent system
c. inconsistent system
