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.