1. Grade Distribution 2nd 5th A 5 B 4 8 C 2 D F 13 7 3 100+ 1 Avg 71.96
No Shows 3
100+ 1
Avg
71.96
76.35 1

2. Using Graphs and Tables to Solve Linear Systems
S E C T I O N
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3-1: Solving Linear Equations through Graphing and Tables

3. 3-1: Solving Linear Equations through Graphing and Tables
Definitions
Systems of Linear Equations
Requires 2 variables into two linear standard form equations
Solutions are systems of ordered pairs (x, y)
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3-1: Solving Linear Equations through Graphing and Tables

4. 3-1: Solving Linear Equations through Graphing and Tables
Example 1
Is (1, 3) a solution to the system,
Plug the coordinates into the system,.
YES
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3-1: Solving Linear Equations through Graphing and Tables

5. 3-1: Solving Linear Equations through Graphing and Tables
Your Turn
Is (–1, 6) a solution to the system,
Plug the coordinates into the system,. NO
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

6. 3-1: Solving Linear Equations through Graphing and Tables
Steps when graphing
Graph both equations (preferably on y-intersect form)
Determine what the intersecting point is and put it in coordinate form
Check your point to both equations
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3-1: Solving Linear Equations through Graphing and Tables

7. 3-1: Solving Linear Equations through Graphing and Tables
Example 2
Graph these equations and determine the intersection points for this system,
Start out with the first equation and put it in y= form
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

8. 3-1: Solving Linear Equations through Graphing and Tables
Example 2
Graph these equations and determine the intersection points for this system,
Find out the second equation and put it in y= form
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

9. 3-1: Solving Linear Equations through Graphing and Tables
Example 2
Graph these equations
(4, 4)
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3-1: Solving Linear Equations through Graphing and Tables

10. 3-1: Solving Linear Equations through Graphing and Tables
Example 2
Check to see if (4, 4) is the accurate solution to the system,…
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

11. 3-1: Solving Linear Equations through Graphing and Tables
Example 3
Graph these equations and determine the intersection points for this system,
Start out with the first equation and put it in y= form
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

12. 3-1: Solving Linear Equations through Graphing and Tables
Example 3
Graph these equations and determine the intersection points for this system,
Find out the second equation and put it in y= form
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

13. 3-1: Solving Linear Equations through Graphing and Tables
Example 3
Graph these equations
(1, 3)
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3-1: Solving Linear Equations through Graphing and Tables

14. 3-1: Solving Linear Equations through Graphing and Tables
Example 3
Check to see if (1, 3) is the accurate solution to the system,…
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

15. 3-1: Solving Linear Equations through Graphing and Tables
Your Turn
Graph these equations and determine the intersection points for this system,
(3, –1)
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3-1: Solving Linear Equations through Graphing and Tables

16. Using Graphing Calculator
Graph these equations and determine the intersection points for this system,
Must be in Y= Form
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3-1: Solving Linear Equations through Graphing and Tables

17. Using Graphing Calculator
Graph these equations and determine the intersection points for this system,
2nd TRACE 5
ENTER
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3-1: Solving Linear Equations through Graphing and Tables

18. 3-1: Solving Linear Equations through Graphing and Tables
Types of Solutions
Put the equations into slope-intercept form
Determine the equation by looking the slope of the system
Determine the solution
Consistent Solution: A system, that has at least ONE solution
Inconsistent Solution: A system, that has NO solution
Independent Solution: A system, that has EXACTLY one solution
Dependent Solution: A system, that has INFINITE amount of solutions
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3-1: Solving Linear Equations through Graphing and Tables

19. 3-1: Solving Linear Equations through Graphing and Tables
Types of Solutions
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3-1: Solving Linear Equations through Graphing and Tables

20. Flowchart INCONSISTENT CONSISTENT INDEPENDENT DEPENDENT
How many solutions does it have?
INCONSISTENT
(No Solution)
CONSISTENT
(At least 1 Solution)
How many points do they intersect?
All points (overlap)
1 point
INDEPENDENT
DEPENDENT
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3-1: Solving Linear Equations through Graphing and Tables

21. 3-1: Solving Linear Equations through Graphing and Tables
Example 4
Graph these equations and determine the intersection points for this system,
Start out with putting both equations into slope-intercept form
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

22. 3-1: Solving Linear Equations through Graphing and Tables
Example 4
Graph these equations and determine the intersection points for this system,
The system, is consistent and dependent with infinitely many solutions.
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3-1: Solving Linear Equations through Graphing and Tables

23. 3-1: Solving Linear Equations through Graphing and Tables
Your Turn
Graph these equations and determine the intersection points for this system,
The system, is inconsistent and has no solution.
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3-1: Solving Linear Equations through Graphing and Tables

24. 3-1: Solving Linear Equations through Graphing and Tables
Example 5
City Park Golf Course charges $20 to rent golf clubs plus $55 per hour for golf cart rental. Sea Vista Golf Course charges $35 to rent clubs plus $45 per hour to rent a cart. For what number of hours is the cost of renting clubs and a cart the same for each course?
11/29/2018 2:06 AM
3-1: Solving Linear Equations through Graphing and Tables

25. 3-1: Solving Linear Equations through Graphing and Tables
Example 5
Let x represent the number of hours and y represent the total cost in dollars.
City Park Golf Course: y = 55x + 20
Sea Vista Golf Course: y = 45x + 35
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3-1: Solving Linear Equations through Graphing and Tables

26. 3-1: Solving Linear Equations through Graphing and Tables
Example 5
Use increments of ½ to represent 30 min.
y = 55x + 20
y = 45x + 35
When x = 1 1/2, the y-values are both The cost of renting clubs and renting a cart for 1 1/2 hours is $ at either company. So the cost is the same at each golf course for 1 1/2 hours. x y 20
47.5 1 75
1 1/2
102.5 2
120 x y 35
57.5 1 80
1 1/2
102.5 2
125
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3-1: Solving Linear Equations through Graphing and Tables

27. 3-1: Solving Linear Equations through Graphing and Tables
Assignment
Pg 156
15-29 odd, 35
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3-1: Solving Linear Equations through Graphing and Tables