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Solving Systems of Linear Inequalities Adapted from Walch Education

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Key Concepts A system of inequalities is two or more inequalities in the same variables that work together. The solution to a system of linear inequalities is the intersection of the half planes of the inequalities. Look for the area where the shading of the inequalities overlaps; this is the solution.

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Practice # 1 Solve the following system of inequalities graphically:

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Graph the line x + y = 10. Use a dashed line because the inequality is non-inclusive Shade the solution set. First pick a test point. Choose a point that is on either side of the line. Test point: (0, 0) Since the point (0, 0) makes the inequality false, shade the opposite side of the line.

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Graph the line 2x 4y = 5 on the same coordinate plane. Use a dashed line because the inequality is non-inclusive Shade the solution set. First pick a test point. Choose a point that is on either side of the line. Test point: (0, 0) Since the point (0, 0) makes the inequality false, shade the opposite side of the line.

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The overlap of the two shaded regions, which is darker, represents the solutions to the system:

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Thanks for Watching !!!!! ~Dr. Dambreville