Explanation Given: The system of inequalities is − x + y ≤ 100 x + 3 y ≤ 150 x ≥ − 80 y ≥ 20 Graph: The graph of the equation − x + y ≤ 100 is drawn by constructing the table for its values for which the inequality is taken as an equation y = 100 + x . For x = 0 , substitute 0 for x . y = 100 + ( 0 ) = 100 For x = − 50 , substitute − 50 for x . y = 100 + ( − 50 ) = 50 For x = 50 , substitute 50 for x . y = 100 + ( 50 ) = 150 Construct the table, using various values of x and y , for the inequality − x + y ≤ 100 . x 0 − 50 50 y 100 50 150 Simplify the inequality x + 3 y ≤ 150 , 3 y ≤ 150 − x y ≤ 150 − x 3 The graph of the equation y ≤ 150 − x 3 is drawn by constructing the table for its values for which the inequality is taken as an equation y = 150 − x 3 . For x = 0 , substitute 0 for x . y = 150 − ( 0 ) 3 = 150 3 = 50 For x = − 30 , substitute − 30 for x . y = 150 − ( − 30 ) 3 = 150 + 30 3 = 180 3 = 60 For x = 30 , substitute 30 for x . y = 150 − ( 30 ) 3 = 120 3 = 40 Construct the table, using various values of x and y , for the inequality x + 3 y ≤ 150 . x 0 − 30 30 y 50 60 40 For the inequality x ≥ − 80 , plot a vertical line, passing through x = − 80 . Similarly, for the inequality y ≥ 20 , plot a horizontal line, passing through y = 20 . To decide the shaded portion for inequality − x + y ≤ 100 , assume a point ( 0 , 0 )

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Author: Crawford

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Chapter 4.4, Problem 28E

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To graph: The system of inequalities, −x+y≤100, x+3y≤150, x≥−80 and y≥20.

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Chapter 4.4, Problem 27E

Chapter 4.4, Problem 29E

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To graph: The system of inequalities, − x + y ≤ 100 , x + 3 y ≤ 150 , x ≥ − 80 and y ≥ 20 .

Solution Summary: The author explains how the system of inequalities, -x+yle 100, is drawn by constructing the table for its values for which the inequality is taken as an equation.

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To graph: The system of inequalities, −x+y≤100, x+3y≤150, x≥−80 and y≥20.

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Chapter 4 Solutions