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# 11_7 - Chapter 11 Systems of Equations and Inequalities...

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Chapter 11 1475 Systems of Equations and Inequalities 11.7 Systems of Inequalities 1. 3 x + 4 < 8 - x 4 x < 4 x < 1 x x < 1 { } or -∞ ,1 ( 29 2. 3 x - 2 y = 6 The graph is a line. x -intercept: 3 x - 2 0 ( 29 = 6 3 x = 6 x = 2 y -intercept: 3 0 ( 29 - 2 y = 6 ⇒ - 2 y = 6 y = - 3 3. x 2 + y 2 = 9 The graph is a circle. Center: (0, 0) ; Radius: 3 4. y = x 2 + 4 The graph is a parabola. x -intercepts: 0 = x 2 + 4 x 2 = - 4, no x - intercepts y -intercept: y = 0 2 + 4 = 4 The vertex has x -coordinate: x = - b 2 a = - 0 2 1 ( 29 = 0. The y -coordinate of the vertex is y = 0 2 + 4 = 4. 5. True 6. y 2 = x 2 , right, 2

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Chapter 11 Systems of Equations and Inequalities 1476 7. satisfied 8. half-plane 9. False 10. True 11. x 0 Graph the line x = 0 . Use a solid line since the inequality uses . Choose a test point not on the line, such as (2, 0). Since 2 0 is true, shade the side of the line containing (2, 0). y –5 5 x –5 5 x 0 12. y 0 Graph the line y = 0 . Use a solid line since the inequality uses . Choose a test point not on the line, such as (0, 2). Since 2 0 is true, shade the side of the line containing (0, 2). y –5 5 x –5 5 y 0 13. x 4 Graph the line x = 4 . Use a solid line since the inequality uses . Choose a test point not on the line, such as (5, 0). Since 5 0 is true, shade the side of the line containing (5, 0). y –5 5 x –5 5 x 4 14. y 2 Graph the line y = 2. Use a solid line since the inequality uses . Choose a test point not on the line, such as (5, 0). Since 0 2 is true, shade the side of the line containing (5, 0). y –5 5 x –5 5 y 2
Section 11.7 Systems of Inequalities 1477 15. 2 x + y 6 Graph the line 2 x + y = 6 . Use a solid line since the inequality uses . Choose a test point not on the line, such as (0, 0). Since 2(0) + 0 6 is false, shade the opposite side of the line from (0, 0). y –2 8 x –2 8 2 x + y 6 16. 3 x + 2 y 6 Graph the line 3 x + 2 y = 6. Use a solid line since the inequality uses . Choose a test point not on the line, such as (0, 0). Since 3(0) + 2(0) 6 is true, shade the side of the line containing (0, 0). y –5 5 x –5 5 3 x + 2 y 6 17. x 2 + y 2 1 Graph the circle x 2 + y 2 = 1. Use a dashed line since the inequality uses >. Choose a test point not on the circle, such as (0, 0). Since 0 2 + 0 2 1 is false, shade the opposite side of the circle from (0, 0). y –5 5 x –5 5 x 2 + y 2 > 1 18. x 2 + y 2 9 Graph the circle x 2 + y 2 = 9. Use a solid line since the inequality uses . Choose a test point not on the circle, such as (0, 0). Since 0 2 + 0 2 9 is true, shade the same side of the circle as (0, 0). y –5 5 x –5 5 x 2 + y 2 9

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Chapter 11 Systems of Equations and Inequalities 1478 19. y x 2 - 1 Graph the parabola y = x 2 - 1. Use a solid line since the inequality uses . Choose a test point not on the parabola, such as (0, 0). Since 0 0 2 - 1 is false, shade the opposite side of the parabola from (0, 0). y –5 5 x –5 5 y x 2 – 1 20. y x 2 + 2 Graph the parabola y = x 2 + 2. Use a dashed line since the inequality uses >.
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11_7 - Chapter 11 Systems of Equations and Inequalities...

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