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Solving Systems of Inequalities Graphically<br>

Learn how to solve a linear system of inequalities in two variables graphically, finding the feasible region bounded by half-planes and vertices. Example problems included.<br>

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Solving Systems of Inequalities Graphically<br>

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  1. 8.5 Systems of Inequalities

  2. A linear system of inequalities in two variables can be solved graphically – the solution is the intersection of the half planes. Solution is called the feasibleregion and its “corners” are the vertices. • Ex 1) Solve the system graphically • 5x + 2y ≤ 10 • 8x + y < 8 • x ≥ 0 • y ≥ 0  y < –8x + 8 • restricts to 1st quadrant

  3. Ex 2) Solve the system graphically • (x – 3)2 – 2 < y • y < │x – 3│

  4. Ex 3) Solve the system graphically • │x + 3y│ < 6 • │2x – y│ > 3 • x + 3y < 6 AND x + 3y > –6 • 2x – y > 3 OR 2x – y < –3 • y < 2x – 3 • y > 2x + 3

  5. Homework #805 Pg 415 #3, 8, 12, 13, 15, 18, 19, 23, 25, 27, 29, 30, 32, 37, 38, 43

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