1. Pre-Calculus 11: Section: 8.1 Solving Systems of Equation by Graphing

2. Review) Graphing a Linear Function
When given a linear function in the form of y=mx+b
The “m” is the slope and the “b” is the y-intercept
Ex: Graph the line:
Start at the y-intercept
Suppose the equation was in general form:
Isolate the Y-variable to get it into standard form:
Then apply the slope to find other points:
Connect the dots

3. I) Solving a Linear System:
In this section, you will be given a system with two equations where each one is a different graph
“Solving” a system of equation means you are finding the “points of intersection” – where the two graphs meet
The coordinates of the “intersection points” will satisfy both equations in the system
When you plug the solution into the original equation, both sides will be equal
2 separate Lines
A Line with a Parabola
Two Separate Parabolas

4. Ex: Solve the System by Graphing
Isolate “y” in each equation
Graph each equation x y -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4
Make a table of Values if the y-intercept is off the graph
The Intersection is:

5. Practice: Solve the System by Graphing
Isolate “y” in each equation
Graph each equation x y -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11
Parabola
Vertex (0,2)
a =1
 1,3,5,7
The Intersections are:

6. Practice: Solve the System by Graphing
Isolate “y” in each equation
Graph each equation x y -6 -4 -2 2 4 6
Parabola
Vertex (2,-3)
a =1
 1,3,5,7
The Intersections are:

7. Ex: Solve the System by Graphing-4 -2 2 4 6 8 10 -6
This is called the
point of tangency.
The Intersection is:

8. Ex: Solve the System by Graphing-6 -4 -2 2 4 6 8
The Intersections are:

9. Homework:
Assignment 8.1