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Graphing a System of Inequalities - Solve and Shade

Learn how to graph a system of inequalities and find the overlapping region. Solve the system x + y ≥ -1 and -2x + y < 2.

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Graphing a System of Inequalities - Solve and Shade

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  1. Do Now Draw the graph of: 2x – 4y > 12

  2. 3 2 1 -3 -2 -1 1 2 3 -1 Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2

  3. Graph 3 2 1 -3 -2 -1 1 2 3 -1 Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2 y ≥ - x - 1 Greater Than Shade Above!!

  4. Graph 3 2 1 -3 -2 -1 1 2 3 -1 Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2 y < 2x + 2 Less Than Shade Below!!

  5. 3 3 2 2 1 1 -3 -3 -2 -2 -1 -1 1 1 2 2 3 3 -1 -1 x + y ≥ -1 -2x + y < 2

  6. 3 2 1 -3 -2 -1 1 2 3 -1 Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y < 2 SOLUTION: • Lies where the two shaded • regions intersect each • other.

  7. Solving Systems of Inequalities • Graph both inequalities on the same graph. • Find the area where the two shaded regions overlap. 3) Mark the solution with anS.

  8. Graph 3 2 y < x - 2 1 -2 -1 1 2 3 4 2 3 Solving a system of Inequalities Consider the system -2x + 3y < -6 5x + 4y < 12 -1 -2

  9. Graph 3 2 y = - x + 3 1 (0,0) -2 -1 1 2 3 4 5 4 Solving a system of Inequalities Consider the system -2x + 3y < -6 5x + 4y < 12  -1 -2

  10. Graph 3 2 1 (0,0) -2 -1 1 2 3 4 Solving a system of Inequalities Consider the system -2x + 3y < -6 5x + 4y < 12 SOLUTION:  • Lies where the two shaded • regions intersect each • other. -1 -2

  11. Graph 3 2 1 (0,0) -2 -1 1 2 3 4 Solving a system of Inequalities Consider the system -2x + 3y < -6 5x + 4y < 12 NOTE:  • All order pairs in dark • region are true in both • inequalities. -1 -2

  12. Graph 6 4 2 (0,0) 2 4 6 8 10 12 -2 -4 -6 Solving a system of Inequalities Consider the system x - 4y ≤ 12 4y + x ≤ 12

  13. Graph 6 4 2 (0,0) 2 4 6 8 10 12 -2 -4 -6 Solving a system of Inequalities Consider the system x - 4y ≤ 12 4y + x ≤ 12

  14. Let’s Try… 2) y + x ≥ 4 y ≤ 2x – 3

  15. Let’s Try… 4) y ≤ 5 x – y > 3

  16. Let’s Try… 3) y + 3x ≥ 6 y < 2x – 4

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