1. Classifying Systems of Linear Equations

2. Types of Systems
There are 3 different types of systems of linear equations
3 Different Systems:
Consistent-independent
Inconsistent
Consistent-dependent

3. Type 1: Consistent-independent
A system of linear equations having exactly one solution is described as being consistent-independent. y
 The system has exactly one solution at the point of intersection x

4. Type 2: Inconsistent
A system of linear equations having no solutions is described as being inconsistent. y
 The system has no solution, the lines are parallel x
Remember, parallel lines have the same slope

5. Type 3: Consistent-dependent
A system of linear equations having an infinite number of solutions is described as being consistent-dependent. y
 The system has infinite solutions, the lines are identical x

6. So basically….
If the lines have the same y-intercept b, and the same slope m, then the system is consistent-dependent
If the lines have the same slope m, but different y-intercepts b, the system is inconsistent
If the lines have different slopes m, the system is consistent-independent

7. Example 1
To solve, rewrite each equation in the form y = mx +b
(1)
(2)
x + 5y = 9
3x – 2y = 12
Isolating y in line (1)
Isolating y in line (2)
x + 5y = 9
3x – 2y = 12
-2y = -3x + 12
5y = -x + 9

8. What type of system is it?
What is the slope and y-intercept for line (1)?
What is the slope and y-intercept for line (2)?
Since the lines have different slopes they will intersect. The system will have one solution and is classified as being consistent-independent.

9. Questions?
Any Questions?
Homework: #1,2,3 – 17  odd numbers only