274 Chapter 3 Systems of Linear Equations and Inequalities y y x 5 4 5 4 1 2 3 4 5 54 2 3 1 2 3 4 5 1 3 1 2 Answers 5. 6. Example 5 demonstrates the union of the solution sets of two linear inequalities. Graphing a Compound Linear Inequality Example 5 Graph the solution set of the compound inequality. 3y 6 or y x 0 Solution: First inequality Second inequality 3y 6 y x 0 y 2 y x The graph of y 2 is the region The inequality y x is of the form on and below the horizontal y mx b. Graph a solid line and the line y 2. See Figure 3-18. region below the line. See Figure 3-19. y 5 4 1 y 5 4 1 The solution to the compound inequality 3y 6 or y x 0 is the union of these regions (Figure 3-20). Skill Practice Graph the solution set. 5. 2y 4 or y x 1 Graphing a Compound Linear Inequality Example 6 Describe the region of the plane defined by the system of inequalities. and Solution: x 0 y 0 for points on the y-axis and in x 0 x 0 the second and third quadrants. for points on the x-axis and in y 0 y 0 the first and second quadrants. The intersection of these regions is the set of points in the second quadrant (with the boundaries included). 5 4 3 2 1 543 1 2 3 4 5 1 Skill Practice Graph the region defined by the system of inequalities. 6. x 0 and y 0 Figure 3-20 x 1 2 3 4 5 54 2 3 1 2 3 4 5 1 3 2 1 Figure 3-18 x 1 2 3 4 5 54 2 3 1 2 3 4 5 1 3 2 Figure 3-19 x 1 2 3 4 5 54 2 3 1 2 3 4 5 1 3 2 y x 21 2 3 4 5 y x 5 4 3 2 1 543 1 2 3 4 5 21 1 2 3 4 5
miller_intermediate_algebra_4e_ch1_3
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