Integrated Math 2 Section 8-2

1. Section 8-2 Solve Systems of Equations Graphically

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. Vocabulary 1. System of Equations: 2. Solution of a System:

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x

42. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x

43. Example 2 Solve the system by graphing. y 2 x − y = 4  x + y = 5 x y = 2 x − 4  y = − x + 5

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. 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. 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. 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. 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. 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. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x

77. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x

78. Example 3 Solve the system by graphing. y = x y  y = −3 y + x = 2  x y = x  y = −3 y = − x + 2 

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. 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. 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. 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. 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. Homework

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

Integrated Math 2 Section 8-2

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