Upcoming SlideShare
×

# Integrated Math 2 Section 8-2

603 views

Published on

Solve Systems of Equations Graphically

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
603
On SlideShare
0
From Embeds
0
Number of Embeds
50
Actions
Shares
0
8
0
Likes
0
Embeds 0
No embeds

No notes for slide
• ### Integrated Math 2 Section 8-2

1. 1. Section 8-2 Solve Systems of Equations Graphically
2. 2. Essential Questions How do you determine if an ordered pair is a solution of a system? How do you solve systems of linear equations graphically? Where you’ll see this: Sports, safety, economics
3. 3. Vocabulary 1. System of Equations: 2. Solution of a System:
4. 4. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System:
5. 5. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System: The intersection of the t wo lines
6. 6. Vocabulary 1. System of Equations: Two or more equations with the same t wo variable that you solve at the same time 2. Solution of a System: The intersection of the t wo lines The ordered pair that makes both equations true
7. 7. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x
8. 8. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x
9. 9. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
10. 10. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
11. 11. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
12. 12. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
13. 13. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
14. 14. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
15. 15. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
16. 16. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
17. 17. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
18. 18. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
19. 19. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
20. 20. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
21. 21. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
22. 22. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
23. 23. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
24. 24. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
25. 25. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
26. 26. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
27. 27. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
28. 28. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
29. 29. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
30. 30. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
31. 31. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
32. 32. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 x y = − x + 7  y = 2 x − 10
33. 33. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. x + y = 7 a. Check by graphing  y 2 x − y = 10 Not a solution x y = − x + 7  y = 2 x − 10
34. 34. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10
35. 35. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7
36. 36. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 7=7
37. 37. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7
38. 38. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10
39. 39. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10 2 = 10
40. 40. Example 1 Tell whether the ordered pair (3, 4) is a solution to the given system. a. Check by substituting the ordered pair into the equations x + y = 7  2 x − y = 10 3+4=7 2(3) - 4 = 10 7=7 6 - 4 = 10 2 = 10 Not a solution
41. 41. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x
42. 42. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x
43. 43. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
44. 44. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
45. 45. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
46. 46. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
47. 47. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
48. 48. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
49. 49. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
50. 50. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
51. 51. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
52. 52. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
53. 53. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
54. 54. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
55. 55. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
56. 56. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
57. 57. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
58. 58. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
59. 59. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
60. 60. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
61. 61. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
62. 62. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
63. 63. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
64. 64. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
65. 65. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
66. 66. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
67. 67. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
68. 68. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
69. 69. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5
70. 70. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 x y = 2 x − 4  y = − x + 5
71. 71. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x y = 2 x − 4  y = − x + 5
72. 72. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4  y = − x + 5
73. 73. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5
74. 74. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5 3+2 = 5
75. 75. Example 2 Solve the system by graphing. y 2 x − y = 4  (3, 2) x + y = 5 Check: x 2(3) − 2 = 4 y = 2 x − 4 6− 2 = 4  y = − x + 5 3+2 = 5
76. 76. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x
77. 77. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x
78. 78. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
79. 79. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
80. 80. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
81. 81. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
82. 82. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 
83. 83. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 x y = x  y = −3 y = − x + 2 
84. 84. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x  y = −3 y = − x + 2 
85. 85. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x A = 16  y = −3 y = − x + 2 
86. 86. Example 3 Solve the system by graphing. y = x y  y = −3 1 y + x = 2 A = bh  2 1 x A = (8)(4) 2 y = x A = 16 units2  y = −3 y = − x + 2 
87. 87. Quick Question If the equations of a system are in slope-intercept form, how can you tell without graphing if the system has a solution?
88. 88. Homework
89. 89. Homework p. 340 #1-27 odd “If the only tool you have is a hammer, you tend to see every problem as a nail.” - Abraham Maslow