Solving Systems of Inequalities

1. Section 1-7 Solving Systems of Inequalities by Graphing

2. Vocabulary 1. System of Inequalities:

3. Vocabulary 1. System of Inequalities: Finding the set of all ordered pairs to satisfy the overlapping shaded regions of two or more inequalities

4. Example 1 Solve the system of inequalities by graphing. y ≥ 2x −3 y < −x + 2 ⎧ ⎨ ⎩ x y

37. Example 2 Solve the system of inequalities by graphing. y ≥ − 3 4 x +1 y ≤ − 3 4 x − 2 ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ x y

52. Example 2 Solve the system of inequalities by graphing. y ≥ − 3 4 x +1 y ≤ − 3 4 x − 2 ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ x y ∅

53. Example 3 Medical professionals recommend that patients have a cholesterol level below 200 milligrams per deciliter (mg/dL) of blood and a triglyceride level below 150 mg/dL. Write and graph a system of inequalities that represents the range of cholesterol levels c and triglyceride levels t for patients.

54. Example 3 Medical professionals recommend that patients have a cholesterol level below 200 milligrams per deciliter (mg/dL) of blood and a triglyceride level below 150 mg/dL. Write and graph a system of inequalities that represents the range of cholesterol levels c and triglyceride levels t for patients. c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

55. Example 3 Solve the system of inequalities by graphing. c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

56. Example 3 Solve the system of inequalities by graphing. c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

57. Example 3 Solve the system of inequalities by graphing. c t c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

58. Example 3 Solve the system of inequalities by graphing. c t c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪

59. Example 3 Solve the system of inequalities by graphing. c t c < 200 t <150 c > 0 t > 0 ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ 50 100 150 200 50 100 150 200

65. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y

66. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1

67. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2

68. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2 3

69. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2 3 x y 0 0 x y 0 0 x y 0 0

70. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2 3 x y 0 0 x y 0 0 x y 0 0 x y 0 1 -0.5 0

71. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2 3 x y 0 0 x y 0 0 x y 0 0 x y 0 1 -0.5 0 x y 0 4 4 0

72. Example 4 Find the coordinates of the vertices of the triangle formed by the following inequalities. 2x −y ≥ −1 x +y ≤ 4 x + 4y ≥ 4 ⎧ ⎨ ⎪ ⎩ ⎪ x y 1 2 3 x y 0 0 x y 0 0 x y 0 0 x y 0 1 -0.5 0 x y 0 4 4 0 x y 0 1 4 0

83. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩

84. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩ 3x = 3

85. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩ 3x = 3 x =1

86. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩ 3x = 3 x =1 1+y = 4

87. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩ 3x = 3 x =1 1+y = 4 y = 3

88. Example 4 2x −y = −1 x +y = 4 ⎧ ⎨ ⎩ 3x = 3 x =1 1+y = 4 y = 3 The three intersection points are (0, 1), (4, 0), and (1, 3)

Solving Systems of Inequalities

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