1. Chapter 5: Systems of Linear Equations
Section 5.4: Solving Special Systems of Linear Equations

2. Key Idea Two lines might not always intercept (parallel)
You can draw one line on top of another line (the same line)
Three Possibilities
One solution (two lines intersect at one point)
No solution (two lines are parallel)
Infinitely Many Solutions (Two equations represent the same line)

3. One Solution
The lines intersect

4. No Solution
The lines are parallel

5. Infinitely many solutions
The lines are the same

6. How do you know when a system gives one, zero, or infinite solutions?
Graph both equations
If using substitution or elimination, and the variables all cancel out:
A false statement at the end indicates the lines are parallel and no solution
A true statement at the end indicates the lines are the same and infinite solutions.

7. Example 1

8. Example 2