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Question: The points (- 3, 0), (2, 0), (0, 3) are joined by line segments to create the polygonal region, then which system of linear inequalities defines the polygonal region? y y x y x y y x y x y y x y x y y x y x Steps to derive 1 Plot the points (- 3, 0), (2, 0), (0, 3) and join by line segments to create a polygonal region.3 Line (1) passes through the points (- 3, 0) and (0, 3).4 m y 2 - y 1 x 2 - x 1 3 - 0 0 - ( - 3 ) 5 As the line (1) crosses y y 6 y m x b 7 y x m b 8 Since, the shaded region is below the solid boundary line (1), the inequality is y x 9 Line (2) passes through the points (0, 3) and (2, 0).10 m y 2 - y 1 x 2 - x 1 0 - 3 2 - 0 3 2 11 Line (2) crosses the y y 12 y m x b 13 y 3 2 x m 3 2 b 14 2y x 15 Since the shaded region is below the solid boundary line (2), the inequality is 2y x 16 The equation of line (3) is y 17 Since the shaded region is above the solid boundary line (3), the inequality is y 18 The system of inequalities that describes the polygonal region is y y x y x Hence the right answer is Option D Click Here To Go Back Instead of multiplying a number by 7, the number is divided by 7. 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