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Copyright © 2010 Pearson Education, Inc. All rights reserved. 4.5 – Slide 5 Solving a System of Linear Inequalities Step 1 Graph the inequalities. Graph each inequality using the method of Section 3.5. Step 2 Choose the intersection. Indicate the solution set of the system by shading the intersection of the graphs (the region where the graphs overlap). Solving Systems of Linear Inequalities by Graphing 4.5 Solving Systems of Linear Inequalities

Copyright © 2010 Pearson Education, Inc. All rights reserved. 4.5 – Slide 6 Example 1 Graph the solution set of the system. Solving Systems of Linear Inequalities by Graphing 5x + 3y ≥ 6 3x – 4y ≤ – 8 To graph 5x + 3y ≥ 6, graph the solid boundary line 5x + 3y = 6. Now, to graph 3x – 4y ≤ – 8, graph the solid boundary line 3x – 4y = – 8. The test point (0, 0) makes this inequality false, so we shade the other side of the boundary. The solution set of this system includes all points in the intersection (overlap) of the graphs of the two inequalities. It includes the shaded region and portions of the two boundary lines shown in the figure. x y 4.5 Solving Systems of Linear Inequalities

Copyright © 2010 Pearson Education, Inc. All rights reserved. 4.5 – Slide 7 Example 2 Graph the solution set of the system. Solving Systems of Linear Inequalities by Graphing x + y > – 2 2x – y < 3 Dashed lines show that the graphs of the inequalities do not include their boundary lines. The solution set of the system is the region with the darkest shading. The solution set does not include either boundary line. x y 4.5 Solving Systems of Linear Inequalities

Copyright © 2010 Pearson Education, Inc. All rights reserved. 4.5 – Slide 8 Example 3 Graph the solution set of the system. Solving Systems of Linear Inequalities by Graphing y ≥ – 2 x ≤ 4 3x – 2y ≥ 6 Recall that x = 4 is a vertical line through the point (4, 0), and y = – 2 is a horizontal line through the point (0, – 2). The graph of the solution set is the shaded region in the figure, including the boundary lines. x y 4.5 Solving Systems of Linear Inequalities