Explanation Given: System of inequalities x + 2 y ≤ 4 2 x − 3 y ≤ 6 x ≥ 0 y ≥ 0 Explanation: Put the inequality equal to zero to make it constraint. The provided inequality is x + 2 y ≤ 4 . x + 2 y = 4 Put x = 0 to find the value of y : 0 + 2 y = 4 2 y = 4 y = 2 Thus, the obtained point to plot the equation is ( 0 , 2 ) . Now, put y = 0 to find the value of x : x + 2 × 0 = 4 x = 4 Thus, the obtained point to plot the equation is ( 4 , 0 ) . Check for the inequality x + 2 y ≤ 4 for the test point ( 0 , 0 ) : 0 + 0 ≤ 4 0 ≤ 4 Thus, the inequality is true for the test point. Therefore, the shaded region is toward the test point. The provided inequality is 2 x − 3 y ≤ 6 . 2 x − 3 y = 6 Put x = 0 to find the value of y : 2 × 0 − 3 y = 6 − 3 y = 6 y = − 2 Thus, the obtained point to plot the equation is ( 0 , − 2 ) . Now, put y = 0 to find the value of x : 2 x − 3 × 0 = 6 2 y = 6 y = 3 Thus, the obtained point to plot the equation is ( 3 , 0 ) . Check for the inequality 2 x − 3 y ≤ 6 for the test point ( 0 , 0 ) : 0 − 0 ≤ 6 0 ≤ 6 Thus, the inequality is true for the test point

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 3, Problem 26RE

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The graph of the system of inequalities x≥0, y≥0, x+2y≤4, and 2x−3y≤6. Also, find all corner points and check whether the region is bounded or not.

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Chapter 3, Problem 25RE

Chapter 3, Problem 27RE

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Chapter 3 Solutions

Finite Mathematics (11th Edition)

Ch. 3.1 - Graph each linear inequality. x + y 2 Ch. 3.1 - Graph each linear inequality. y x + 1 Ch. 3.1 - Graph each linear inequality. x 2 y Ch. 3.1 - Graph each linear inequality. y x 3 Ch. 3.1 - Graph each linear inequality. 4x y 6 Ch. 3.1 - Graph each linear inequality. 4y + x 6 Ch. 3.1 - Graph each linear inequality. 7. 4x + y 8 Ch. 3.1 - Graph each linear inequality. 2x y 2 Ch. 3.1 - Graph each linear inequality. x + 3y 2 Ch. 3.1 - Graph each linear inequality. 2x + 3y 6

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The graph of the system of inequalities x ≥ 0 , y ≥ 0 , x + 2 y ≤ 4 , and 2 x − 3 y ≤ 6 . Also, find all corner points and check whether the region is bounded or not.

Solution Summary: The author explains how to determine the graph of the system of inequalities and determine whether the region is bounded or not.

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The graph of the system of inequalities x≥0, y≥0, x+2y≤4, and 2x−3y≤6. Also, find all corner points and check whether the region is bounded or not.

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Chapter 3 Solutions