3.1 Graphing Systems of Equations

1
3.1 Graphing Systems of Equations
2
What is a system?

• Two Equations and two unknowns
• Examples
• y3x5 or 2x 7y 19
• Y5x-2 3x -9y -1

3
Types of SystemsConsistent and Independent

• 1) y 3x 3
• y -2x 7

One Intersection One solution
4
Types of SystemsConsistent and Dependent

• 1) 2x 4y 12
• 4x 8y 24

Infinite intersections Infinite solutions
5
Types of SystemsInconsistent

• 1) y 2x 3
• y 2x 2

No Intersection No solution
6
Practice Solve the system of equations by
graphing. Then categorize the solution.

• yx3
• Y-2x3

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.

• 3xy5
• 15x5y2

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.

• y2x3
• -4x2y6

Infinite Solutions Dependent (same line)
Question how could we see that graphs would be
the same line without graphing them?
9
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
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.