1. 6.1 Solving Systems Of Equations By Graphing

2. Bell Work Evaluate each expression for x = 1 and y = –3.
1. x – 4y –2x + y
Write each expression in slope-intercept form.
3. y – x = 1
4. 2x + 3y = 6 5.

3. Cheetah Vs. Usain Bolt
Video:

4. Distance
(5.95, 100)
Bolt=
Cheetah=
100 m
(9.58, 100)
9 10
Time

5. Distance
Bolt=
Cheetah=
100 m
(9.58, 100)
40 m
9 10
Time

6. Solving Linear Equations By Graphing
Our goal is to;
Graph TWO lines on same graph
Locate where they intersect (or if they do at all)

7. Solving a Linear Equation
Linear equations can look like;
y = 3x + 7 Or
-3x + y = 7
7 + 3x = y …

8. 3 Graphing Possibilities
Intersecting Lines
Parallel Lines
Coinciding Lines

9. 1) Intersecting Lines
The point where the lines intersect is your solution.
The solution of this graph is (1, 2)
(1,2)

10. What is the solution of the system graphed below?
(2, -2)
(-2, 2)
No solution
Infinitely many solutions

11. Where do these graphs intersect

12. 2) Parallel Lines These lines never intersect!
Since the lines never cross, there is NO SOLUTION!
Parallel lines = SAME SLOPE, different y-int.

13. Our Slopes Must Be Twins!!!
Parallel Lines
Hi, I’m Two
Hey, I’m Two Too!
Our Slopes Must Be Twins!!!

14. What is the solution of this system?
y = 3x + 3
y = 3x - 12
(3, -12)
Parallel solutions
No solution
Infinitely many solutions

15. 3) Coinciding Lines These lines are the same!
Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS!
Coinciding lines = SAME SLOPE, SAME Y-INT.

16. What is the solution of this system?
y = 3x - 8
(3, 1)
(4, 4)
No solution
Infinitely many solutions

17. Problem-Solving Application
Sally and Jenni are reading the same book. Wren is on page 14 and reads 2 pages every night. Jenni is on page 6 and reads 3 pages every night. After how many nights will they have read the same number of pages? How many pages will that be?
pages
Time

18. 
(8, 30)
Nights

19. Lets try one: Find the solution to the following system:
y = -2x+4
y = x -2
m= b=4
m=1 b=-2
Step 1:Graph both equations
Step 2: Find
Where the lines intersect?
THE SOLUTION: (2,0)

20. Check your answer! Y=-2x+4 2(2) + 4 = 0 y = x-2 (2) – 2 = 0
To check your answer, substitute the point back into both equations.
Y=-2x+4
2(2) + 4 = 0
y = x-2
(2) – 2 = 0

21. You try: Where do the lines intersect?
y = 2x – 1
y = –x + 5
Graph both equations
Where do they intersect?
The point is (2, 3)

22. Try again: Find the solution to the system
y = -2x-1
y = -2x+4
Graph both equations
Where do they intersect?
NO SOLUTION

23. Find the Solution

24. Summary Intersecting Lines have how many solutions?
Parallel Lines have the same what?
How can you tell if two equations are coinciding without graphing them?
Do you have to graph the system to know the answer if both equations have the same slope?

25. HOMEWORK
Find an example in real life (just like Usain Bolt vs. Cheetah) and graph it.
I want to see the following
What two things are you graphing
What is your x-axis and y-axis
Graph them
Do they intersect? Where?

26. Challenge: Find the solution to the following system:
y = 2x – 3
-2x + y = 1
Graph both equations.
Put both equations in slope-intercept
y=mx+b
y = 2x + 1
Graph using slope and y-intercept

27. Graph the equations. y = 2x – 3 m = 2 and b = -3 y = 2x + 1
Where do the lines intersect?
No solution!
Notice that the slopes are the same with different y-intercepts. If you recognize this early, you don’t have to graph them!