Download 3.1 Graphing systems of equations

3.1 Graphing Systems of
Equations
What is a system?
• Two Equation’s and two
unknowns
• Examples:
• y=3x+5
• Y=5x-2
or
2x + 7y = 19
3x -9y = -1
Types of Systems
Consistent and Independent
1)
2)
y = 3x – 3
y = -2x + 7
One Intersection
One solution
Types of Systems
Consistent and Dependent
1)
2)
2x + 4y = 12
4x + 8y = 24
Infinite intersections
Infinite solutions
Types of Systems
Inconsistent
1)
2)
y = 2x – 3
y = 2x + 2
No Intersection
No 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 Graphing
In 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.