1. 5.1 Graphing Systems of Equations
System of linear Equations: Two or more linear equations together.
Examples:

2. Solving a system of equations by GRAPHING!
The solution of a system is…
A. The point where the two lines intersect on the graph.
B. An ordered pair that makes all the equations in the system true.
No Intersection
No Solution
Solution

3. Number of Solutions
When you have 2 or more equations on the same graph.
A set of ordered pairs that works for both equations.
When the graphs intersect or coincide – has at least one solution.
The graphs are parallel – there is no solution.
One Solution
Infinite number of solutions (same line!)
System of Equations
Solution
Consistent
Inconsistent
Independent
Dependent

4. Intersecting Lines Number of Solutions: Exactly One (1)
Equations with different slopes are intersecting lines!
Consistent & Independent
Solution
Solution

5. Parallel Lines Number of Solutions: Zero (0)
Equations with the same slope are parallel lines!
Inconsistent

6. Same Lines (Co-linear or Overlapping)
Number of Solutions: Infinitely Many
Equations with the exact same slope and y-intercept are the same line!!
Consistent & Dependent

7. Link to Smartboard Examples