1. 6.1 Graphing Systems of Equations
Objective:
Determine the number of solutions a system of linear equations has
Solve systems of linear equations by graphing

2. How do we graph a Linear Equation
Linear Equation- y=mx + b
1) Find the y-intercept
2) Use the slope to find your next point
3) Draw a line through the two points

3. What is a system of equations?
A "system" of equations is a set of 2 or more equations that we solve as one.

4. Inconsistent- a system that has no solution
Vocabulary
Consistent- a system that has at least one solution. The graphs intersect at one point or are the same line.
Inconsistent- a system that has no solution V

5. Vocabulary
Independent- a consistent system that has exactly one solution
Dependent- a consistent system that has an infinite number of solutions

6. Possible Solutions
Page 334 Example 1 # a and b and c

7. You Try
Page 336 #1-6

8. Finding a Solution by Graphing
Graph the equations carefully on the same coordinate plane
Find their point of intersection
a) This point is the solution of the system

9. Example 1
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
y = -3x +10
y = x –2

11. Example 2
Graph the system and determine the solution to the system.
2x - y = -1
4x – 2y = 6

12. Example 3
y = -2x – 3
6x + 3y = -9

13. You Try
Page 336 # 7 and 8

14. Write and Solve a System of Equations
Naresh rode 20 miles last week and plans to ride 35 miles per week. Diego rode 50 miles last week and plans to ride 25 miles per week. Predict the week in which Naresh and Diego will have ridden the same number of miles.

15. Write and Solve a System of Equations
Joe and Josh each want to buy a video game. Joe has $14 and saves $10 a week. Josh has $26 and saves $7 a week. In how many weeks will they have the same amount?

16. You Try
Page 336 #9

17. Journal
Describe the advantages and disadvantages to solving systems of equations by graphing

18. Class work
Page 336 # odd