1. 3.1 Graphing Systems of Equations

2. What is a system? Two Equation’s and two unknowns Examples: y=3x+5or2x + 7y = 19 Y=5x-23x -9y = -1

3. Types of Systems Consistent and Independent 1) y = 3x – 3 2) y = -2x + 7 One Intersection One solution

4. Types of Systems Consistent and Dependent 1) 2x + 4y = 12 2) 4x + 8y = 24 Infinite intersections Infinite solutions

5. Types of Systems Inconsistent 1) y = 2x – 3 2) y = 2x + 2 No Intersection No solution

6. Practice – Solve the system of equations by graphing. Then categorize the solution. y=x+3 Y=-2x+3 One solution - Independent Question: how could we see the intersection of this system with without graphing it?

7. Practice – Solve the system of equations by graphing. Then categorize the solution. 3x+y=5 15x+5y=2 No Solutions – Inconsistent (Parallel lines) Question: how could we see the lack of an intersection of this system with without graphing it?

8. Practice – Solve the system of equations by graphing. Then categorize the solution. y=2x+3 -4x+2y=6 Infinite Solutions – Dependent (same line) Question: how could we see that graphs would be the same line without graphing them?

9. Classifying Systems without Graphing In your own words, come up with clues that would help you determine the number of solutions for each situation One solutionNo solutionsInfinite solutions

10. For Next Class: Print a copy of Graphing Parametric Equations on the Graphing Calculator from the Graphing Calculator Cheat Sheet web page on the class web site.