1. Bellwork 1.) How many different ways can 2 lines appear on a graph?
2.) What are they?
3.) How many solutions are there for each of the different ways 2 lines can appear on a graph?

2. Objective
To be able to determine the number of solutions of a system of equations by either solving by graphing or substitution.

3. Graph y = x + 3 & 2y = 2x + 6 2y = 2x + 6 y = x + 3 Solution= infinite

4. Solve by Substitution y = x + 3 2y = 2x + 6 So…..
2(x + 3) = 2x + 6 (Distribute 2)
2x + 6 = 2x + 6 (Subtract 2x)
6 = 6
Solution = infinite

5. Graph y = 3x + 1 & 4y -12x = 8 4y - 12x = 12 y = 3x + 1 Solution= none

6. Solve by Substitution y = 3x + 1 4y - 12x = 8 So…...
4(3x + 1) - 12x = 8(Distribute 4)
12x x = 8 (C L T)
4 = 8
Solution = none

7. Identifying the solutions
There are 3 ways 2 lines can appear on a graph.
1.) They cross at 1 point
2.) They are Parallel
3.) They are the same line

8. Identifying the solutions
1.) They cross at 1 point (2, -4) One
2.) They are Parallel 4 = 8 None
3.) They are the same line 6 = 6 Infinite

9. Identify the # of solutions
1.) 7=7
2.) (2,3)
3.) 4=-4
4.) 0=0
1.) Infinite
2.) One
3.) None
4.) Infinite

10. Identify the # of solutions
5.) 0=5
6.) 2=3
7.) (4,-4)
8.) 6=6
5.) None
6.) None
7.) One
8.) Infinite

11. Graph and find the # of Solutions
1.)x - y = 3
x - y = -2
1.)y = x -3
y = x + 2

12. Graph y = x y = x + 2 Y X
Solution= none

13. Classwork
Do Worksheet 7-5
Homework
Page 377 (1-15 )