1. Algebra 1 Notes Lesson 7-1 Graphing Systems of Equations

2. Mathematics Standards
Patterns, Functions and Algebra: Generalize patterns using functions or relationships, and freely translate among tabular, graphical and symbolic representations.
Patterns, Functions and Algebra: Describe problem situations by using tabular, graphical, and symbolic representations.
Patterns, Functions and Algebra: Demonstrate the relationship among zeros of a function, roots of equations and solutions of equations graphically and in words.

3. Mathematics Standards
Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
Patterns, Functions and Algebra: Solve real-world problems that can be modeled using systems of linear equations and inequalities.

4. Vocabulary Ex/ 2x + 3y = 5 y = -4x + 6
System of Equations – Two or more equations together
Ex/ 2x + 3y = 5
y = -4x + 6
Solution to Systems – Ordered pair that makes both equation true
Three possibilities

5. Vocabulary 1)Exactly one solution – equations make intersecting lines
System of Equations – Two or more equations together
1)Exactly one solution – equations make intersecting lines

6. Vocabulary 1)Exactly one solution – equations make intersecting lines
System of Equations – Two or more equations together
1)Exactly one solution – equations make intersecting lines
The one solution is
where the lines intersection. (x,y)

7. Vocabulary 2) Infinitely many solutions – equations make the same line
System of Equations – Two or more equations together
2) Infinitely many solutions – equations make the same line

8. Vocabulary 2) Infinitely many solutions – equations make the same line
System of Equations – Two or more equations together
2) Infinitely many solutions – equations make the same line
“Infinitely many solutions”

9. Vocabulary
System of Equations – Two or more equations together
3) No solutions – equations make lines that DON’T intersect (parallel)

10. Vocabulary
System of Equations – Two or more equations together
3) No solutions – equations make lines that DON’T intersect (parallel)
“No solutions”

11. Work the next two examples on your own paper

12. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

13. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

14. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

15. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

16. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

17. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

18. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x - 7

19. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
intersection

20. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
intersection

21. Example 1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
y = -x + 8
y = 4x – 7
Find the point of
Intersection (3,5)

22. Example 2
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions.
x – 2y = 4
x – 2y = -2

23. Example 2 x – 2y = 4 x – 2y = -2 – x – x -2y = 4 – x -2 -2 y = -2 + ½x
y = -2 + ½x
y = ½x – 2

24. Example 2 x – 2y = 4 x – 2y = -2 – x – x – x – x -2y = 4 – x -2 -2
y = -2 + ½x
y = ½x – 2

25. Example 2 x – 2y = 4 x – 2y = -2 – x – x – x – x
y = -2 + ½x
y = ½x – 2

26. Example 2 x – 2y = 4 x – 2y = -2 – x – x – x – x
y = -2 + ½x
y = ½x – 2

27. Example 2 x – 2y = 4 x – 2y = -2 – x – x – x – x
y = -2 + ½x y = 1 + ½x
y = ½x – 2

28. Example 2 x – 2y = 4 x – 2y = -2 – x – x – x – x
y = -2 + ½x y = 1 + ½x
y = ½x – y = ½x + 1

29. Example 2
y = ½x – y = ½x + 1
No Solution

30. Now go back to the guided notes

31. Story Problem
Mr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X –
Y -

32. Story Problem
Mr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X – ride time
Y -

33. Story Problem
Mr. Clem went on a 20 mile “bike-hike” that lasted 3 hours. His hiking speed was 4 mph, and his riding speed was 12mph. How long did he walk? How long did he ride?
X – ride time
Y - walk time
x + y = 3
12x + 4y = 20

34. Story Problem
x + y = x + 4y = 20
– x – x
y = -x + 3

35. Story Problem
x + y = x + 4y = 20
– x – x – 12x – 12x
y = -x + 3

36. Story Problem x + y = 3 12x + 4y = 20 – x – x – 12x – 12x

37. Story Problem x + y = 3 12x + 4y = 20 – x – x – 12x – 12x
y = -3x + 5

38. Story Problem y = -x + 3 y = -3x + 5 x = hours rode y = hours walked
They walked for 2 hours.
They rode for 1 hour.
(1, 2)

39. Homework
Pgs. 372
16-40 (evens) (all)