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Section 3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables 273 y x 4 3 2 3 4 5 54 2 2 1 3 5 1 1 2 3 4 5 1 2. Compound Linear Inequalities in Two Variables Some applications require us to find the union or intersection of the solution sets of two or more linear inequalities. y 7 x 1 x y 6 1 12 Example 4 y 7 x y 6 1 12 y 6 x 1 x 1 y 7 mx b. y 6 mx b. y 1 5 4 3 2 1 1 2 3 4 5 54 2 Graphing a Compound Linear Inequality 1 2 3 4 5 Figure 3-14 x 3 The region bounded by the inequalities is the region above the line y x 1 and below the line y x 1. This is the intersection or “overlap” of the two regions (shown in purple in Figure 3-16). 12 12 y x 1 5 4 3 1 Figure 3-16 y x 1 y x 1 2 3 4 5 54 2 2 1 2 3 4 5 1 3 y 5 4 3 1 The intersection is the solution set to the system of inequalities. See Figure 3-17. y 5 4 3 1 Figure 3-17 x 1 2 3 4 5 54 2 2 1 2 3 4 5 1 3 Answer 4. Skill Practice Graph the solution set. 4. x 3y 7 3 and y 6 2x 4 Figure 3-15 x 1 2 3 4 5 54 2 2 1 2 3 4 5 1 3 Graph the solution set of the compound inequality. and Solution: Solve each inequality for y. First inequality Second inequality The inequality is of the form The inequality is of the form Shade abovethe Shadebelow the boundary line. See Figure 3-14. boundary line. See Figure 3-15.


miller_intermediate_algebra_4e_ch1_3
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