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7.4 Systems of Inequalities

7.4 Systems of Inequalities. Shading in the region of possible answers. System of Inequalities. y ≥ 2x – 3 y < - x + 2 We graph both inequalities and find where the shaded area overlap. System of Inequalities. y ≥ 2x – 3 y < - x + 2 Where do we shade?. System of Inequalities.

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7.4 Systems of Inequalities

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  1. 7.4 Systems of Inequalities Shading in the region of possible answers

  2. System of Inequalities y ≥ 2x – 3 y < - x + 2 We graph both inequalities and find where the shaded area overlap

  3. System of Inequalities y ≥ 2x – 3 y < - x + 2 Where do we shade?

  4. System of Inequalities y ≥ 2x – 3 y < - x + 2 Where do we shade? The answers Are in the Overlapped area

  5. Solve y ≤ - x + 1 | x + 1| < 3

  6. Solve y ≤ - x + 1 | x + 1| < 3 is – 3 < x + 1<3

  7. Solve y ≤ - x + 1 | x + 1| < 3 is – 3 < x + 1<3 • 3 < x + 1 • 4 < x • and x + 1 < 3 x < 2

  8. Solve y ≤ - x + 1 | x + 1| < 3 is – 3 < x + 1<3 • 3 < x + 1 • 4 < x • and x + 1 < 3 x < 2 Shade in the region

  9. This system is y ≥ - ¾x + 1different: y ≤ - ¾ x - 2 Shade the Inequalities

  10. This system is y ≥ - ¾x + 1different: y ≤ - ¾ x - 2 Shade the Inequalities. Where are The answers?

  11. Can we find the points where the lines cross making a vertices? Of course, we use substitution or elimination. With three lines a region can be closed in.

  12. 2x – y ≥ - 1x + y ≤ 4x + 4y ≥ 4 - y ≥ -2x – 1 y ≤ 2x + 1 x + y ≤ 4 y ≤ - x + 4 4y ≥ - x + 4 y ≥ - ¼x + 1

  13. 2x – y ≥ - 1x + y ≤ 4x + 4y ≥ 4 y ≤ 2x + 1 y ≤ - x + 4 y ≥ - ¼x + 1 Where do we shade ?

  14. Lets Graph Where are the answers?

  15. Lets Graph Where are the answers?

  16. Homework Page 519-522 # 6, 18, 30, 42, 48, 62, 76, 92

  17. Homework Page 519-522 # 12, 24, 36, 44, 54, 68, 88

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