1. 3.1.1 – Solving Systems by Graphing

2. A third method we can use to find the solutions to systems is through graphing
Graphing generally is a last resort, but when given the equations already graphed, much easier to locate the solution values

3. Solutions To find the solutions to a system by graphing, we look
for the point of intersection
The ordered pair on the Cartesian grid (x, y) are the solutions to the system
When finding these solutions, very important to go back and check for the proper answer by plugging values back in

4. Three types of solutions, like that with elimination:
1) One Solution
2) Infinite Solutions
3) No Solutions

5. To find the solutions, you may have to graph both equations
If not already given the graph, remember, for y = mx + b
b is the y-intercept, or starting point
The slope m, rise/run, allows you to find a second point

6. Example. Find the solution to the given system.
Do the lines intersect?
x and y coordinates?

7. Example. Find the solution to the given system.
Do the lines intersect?
x and y coordinates?

8. Example. Find the solution to the given system.
Do the lines intersect?
x and y coordinates?

9. Example. Find the solutions to the following system:
y = -x – 1
y = -3x + 5

10. Example. Find the solutions to the following system:
y = (-1/2)x - 1
y = (1/2)x - 3

11. Example. Find the solutions to the following system:
y = 2x + 4
y = 2x - 1

12. Word Problems We can also use elimination when writing word problems
Example. An online store is older albums for download, a pack of 5 for $5 and a pack of 10 for $8. You buy 45 albums to download for $37. How many of each pack did you buy?

14. Assignment
Pg. 128
3, 5, 8-10, 14-16, 23-25, 26, 29, 35, 39