3.1 Graphing Systems of Equations
What is a system?
• Two Equation’s and two unknowns
• Examples: • y=3x+5 or 2x + 7y = 19• Y=5x-2 3x -9y = -1
Types of SystemsConsistent and Independent
1) y = 3x – 3 2) y = -2x + 7
One IntersectionOne solution
Types of SystemsConsistent and Dependent
1) 2x + 4y = 122) 4x + 8y = 24
Infinite intersectionsInfinite solutions
Types of SystemsInconsistent
1) y = 2x – 3 2) y = 2x + 2
No IntersectionNo solution
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?
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?
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?
Classifying Systems without GraphingIn your own words, come up with clues that would help you
determine the number of solutions for each situation
One solution No solutions Infinite solutions
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.