Explanation Given Information: The provided inequalities are 3 x + 2 y ≤ 6 , 3 x − 2 y ≥ 6 and − y ≥ 2 . Graph: Consider the provided inequalities are 3 x + 2 y ≤ 6 , 3 x − 2 y ≥ 6 and − y ≥ 2 , Consider the inequality 3 x + 2 y ≤ 6 , Assume the equation as, 3 x + 2 y = 6 Now, substitute the values of x in order to get the corresponding values of y and sketch the graph of the line. For x = 0 3 ( 0 ) + 2 y = 6 y = 3 Therefore, the point is ( 0 , 3 ) For x = 1 3 ( 1 ) + 2 y = 6 y = 3 2 Therefore, the point is ( 1 , 3 2 ) For x = 2 3 ( 2 ) + 2 y = 6 y = 0 Therefore, the point is ( 2 , 0 ) The points for the equation 3 x + 2 y = 6 are as follows: x y ( x , y ) 0 3 ( 0 , 3 ) 2 0 ( 2 , 0 ) 1 3 2 ( 1 , 3 2 ) The graph of the inequality is as follows: Hence, the boundary points for the equation are ( 2 , 0 ) and ( 0 , 3 ) Consider the inequality 3 x − 2 y ≥ 6 , Assume the equation as, 3 x − 2 y = 6 For x = 0 3 ( 0 ) − 2 y = 6 y = − 3 Therefore, the point is ( 0 , − 3 ) For x = 1 3 ( 1 ) − 2 y = 6 y = − 3 2 Therefore, the point is ( 1 , − 3 2 ) For x = 2 3 ( 2 ) − 2 y = 6 y = 0 Therefore, the point is ( 2 , 0 ) The points for the equation 3 x − 2 y = 6 are as follows: x y ( x , y ) 0 − 3 ( 0 , − 3 ) 1 − 3 2 ( 1 , − 3 2 ) 2 0 ( 2 , 0 ) The graph of the inequality is as follows: Hence, the boundary points are ( 0 , − 3 ) and ( 2 , 0 ) Now, consider − y ≥ 2 , Assume the equation as, − y = 2 , The equation points towards the line parallel to x- axis at ( 0 , − 2 ) The simultaneous graph for the given equations can be determined by the inequality principle

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6.1, Problem 16E

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To graph: The inequalities 3x+2y≤6, 3x−2y≥6 and −y≥2 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

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Chapter 6 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - In Exercises 1-26, sketch the region that...Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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To graph: The inequalities 3 x + 2 y ≤ 6 , 3 x − 2 y ≥ 6 and − y ≥ 2 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

Solution Summary: The author explains how to graph the inequalities 3x+2yle 6,3x-2y

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To graph: The inequalities 3x+2y≤6, 3x−2y≥6 and −y≥2 and also check whether the region of the inequalities are bounded or unbounded and find the coordinates of all the corner points if possible.

Chapter 6 Solutions