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7.5

7.5. Systems of Linear Inequalities. Procedure for Solving a System of Linear Inequalities.

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7.5

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  1. 7.5 Systems of Linear Inequalities

  2. Procedure for Solving a System of Linear Inequalities 1. Select one of the inequalities. Replace the inequality symbol with an equals sign and draw the graph of the equation. Draw the graph with a dashed line if the inequality is < or > and with a solid line if the inequality is ≤ or ≥. 2. Select a test point on one side of the line and determine whether the point is a solution to the inequality. If so, shade the area on the side of the line containing the point. If the point is not a solution, shade the area on the other side of the line.

  3. Procedure for Solving a System of Linear Inequalities continued 3. Repeat steps 1 and 2 for the other inequality. 4. The intersection of the two shaded areas and any solid line common to both inequalities form the solution set to the system of inequalities.

  4. Graph the following system of inequalities and indicate the solution set. Solution: Graph both inequalities on the same axis. The first graph will have a dashed line and the second graph a solid line. Example: Solving a System of Inequalities

  5. Practice Problem: solve the system of inequality by graphing.x + y > 22x – y < 4

  6. Example: Another System of Inequalities Graph the following system of inequalities and indicate the solution set. Solution: Graph both on the same axes. The solution set is the region of the graph that is shaded in both colors. The point of intersection is not part of the solution because it does not satisfy the inequality y < 1.

  7. Homework: p. 423 #5 – 20 all • Must be done on graph paper. • Ch. 7.2 quiz next class

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