1. SWBAT… Solve a system of equations using the graphing method Tues, 2/5
Agenda
WU (5 min)
Notes (15 min)
Graphing method posters (30 min)
Warm-Up:
Set-up your notes – Topic is “System of Equations – Graphing Method”
HW#1: Systems - Graphing

2. We are starting a new unit: System of Linear Equations & Inequalities
SWBAT…
Solve a system of linear equations using the graphing method
Solve a system of linear equations using the substitution method
Solve a system of linear equations using the elimination method (adding, subtracting, or multiplying)
Write and solve a system of equations based on real life scenarios (application word problems)
Solve a system of linear inequalities using the graphing method
(~4 week unit)

3. What should I already know to be successful in this unit (pre-requisite skills)?
Distributive property
Combining like terms
Solving a multi-step equation
Solving a literal equation
Finding the slope and y-intercept of lines
Graphing lines (solving for y)
Writing equations of lines in slope-intercept form
Writing and finding ordered pairs
Parallel lines and intersecting lines

4. MT = T + Th + R206 + R208 MT = Math Tutoring T = Tuesday Th = Thursday
R206 = Room 206
R208 = Room 208
MT = T + Th + R206 + R208

5. System of Equations: Graphing Method
What is a system of equations?
A collection of equations involving the same set of variables.
We will be dealing with two equations and two variables.
x – y = 2
3y + 2x = 9

6. Solving Systems of Equations: Graphing Method
Step 1) Write the equations of the lines in slope intercept form.
Step 2) Graph each line on the same graph.
Step 3) Determine the point of intersection and write this point as an ordered pair.
If the two equations have no points in common, the system of equations has no solution.
Parallel lines; same m and different b
If the two equations represent the same line, the system of equations has infinitely many solutions.
Same line; same m and same b
Step 4) If there is one solution, check your work. Substitute the ordered pair for x and y in each equation.

7. Example
Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution and check your answer.
x – y = 2
3y + 2x = 9
Step 1: Write each equation in slope-intercept form.
3y + 2x = 9
-2x -2x
x – y = 2
-x -x
3y = -2x + 9
-y = -x + 2 3 3 3 -1 -1 -1
y = x – 2

8. Step 2: Graph each line on the same graphx y
Step 3: Determine the point of intersection.
(3,1).
y = x – 2
This system of equations has one solution, the point (3, 1).
3 – 1 = (1) + 2(3) = 9
2 = = = 9
Step 4: Check your answer

9. Activity-System of equations – Graphing Method
You and a partner will be given a system of equations to graph on poster board
Directions:
Solve the system using the graphing method (show work on poster)
Determine the number of solutions it has
If the system has one solution, name it
If the system has one solution, check your answer

10. SWBAT… Solve a system of equations using the graphing method Wed, 2/6
Agenda
WU (15 min)
Conclusions about graphing method and solutions (25 min)
Review HW#1 (10 min)
Warm-Up:
What are advantages and disadvantages to the graphing method.
1. Sample Answer: Graphing clearly shows whether a system of equations has one solution, no solution, or infinitely many solutions. However, finding the exact values of x and y from a graph can be difficult.
2. Yes = and 4 = 4

11. Disadvantage to graphing?
Graphing clearly shows whether a system of equations has one solution, no solution, or infinitely many solutions.
It’s visual!
Disadvantage to graphing?
Finding the exact values of x and y from a graph can be difficult. 11

12. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions

13. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
One solution

14. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
Different slope (m)
Same or different y-intercept (b)
Intersecting lines
One solution

15. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
Different slope (m)
Same or different y-intercept (b)
Intersecting lines
One solution
No Solution

16. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
Different slope (m)
Same or different y-intercept (b)
Intersecting lines
One solution
Same slope (m)
Different y-intercept (b) 
Parallel lines 
No Solution

17. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
Different slope (m)
Same or different y-intercept (b)
Intersecting lines
One solution
Same slope (m)
Different y-intercept (b) 
Parallel lines 
No Solution
Infinite Solutions

18. Compare slope (m) and the y-intercept ( b)
Types of lines
Picture /Diagram
Number of solutions
Different slope (m)
Same or different y-intercept (b)
Intersecting lines
One solution
Same slope (m) but
Different y-intercept (b) 
Parallel lines 
No Solution
 Same slope (m) and
Same y-intercept (b)
Same lines
Infinite Solutions

19. Additional Examples
Graph the system of equations. Determine whether the system has one solution, no solution, or infinitely many solutions. If the system has one solution, determine the solution.

20. Lines Intersect y The two equations in slope-intercept form are: x
The point of intersection of the two lines is the point (3, 0).
This system of equations has one solution, the point (3,0).

21. Lines Do Not Intersect Parallel Linesx y
The two equations in slope-intercept form are:
This system of equations represents two parallel lines.
This system of equations has no solution because these two lines have no points in common.

22. Lines that are the Same yx y
The two equations in slope-intercept form are:
These two equations represent the same line.
Therefore, this system of equations has infinitely many solutions.

23. HW#1: Systems-Graphing Method Answers:
1 Solution: (1, 2)
1 Solution: (-4, -2)
Infinite Solutions
1 Solution: (-2, -2)
Solution
No Solution

24. Exit Slip
Find the solution to the below system of equations using the graphing method.
(Hint: Write each equation in slope-intercept form)
How many solutions exist? Write the solution as an ordered pair.
Check your answer.
y – 2x = 6
-4y – 4x = 12