Explanation The given linear inequalities are, 6 x − 4 y > 8 (1) 2 x + 5 y < 5 (2) Consider the equation (1). Since the given inequality in the equation is >, the points on the line do not satisfy the inequality. Hence, the dashed line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation (1) with an “equals” sign. Then the equation (1) becomes, 6 x − 4 y = 8 . Rewrite the above equation. − 4 y = 8 − 6 x y = − 8 4 + 6 x 4 y = 3 x 2 − 2 Obtain any 2 coordinates from the above equation to draw the line. Consider x = 0 , 4 3 and obtain the corresponding values of y . Substitute x = 0 in the linear equation y = 3 x 2 − 2 , y = 3 ( 0 ) 2 − 2 y = − 2 The value of y is − 2 when x = 0 . Thus, the first coordinate is ( 0 , − 2 ) . Substitute x = 4 3 in the linear equation y = 3 x 2 − 2 , y = 3 ( 4 3 ) 2 − 2 y = 2 − 2 y = 0 The value of y is 0 when x = 4 3 . Thus, the second coordinate is ( 4 3 , 0 ) . Use the test point to determine the half plane which is to be shaded. Let the test point be ( 0 , 0 ) . Now substitute the test point ( 0 , 0 ) in 6 x − 4 y > 8 , 6 ( 0 ) − 4 ( 0 ) > 8 0 > 8 It is noticed that the inequality 6 x − 4 y > 8 is false for the test point. Thus, shade the half-plane that does not contains the test point ( 0 , 0 ) . That is, the half-plane above the line. Let us consider the equation (2). Since the given inequality in the equation is < , the points on the line do not satisfy the inequality. Hence, the dashed line is used to join the coordinates of this equation. Now, replace the inequality symbol in the given equation (2) with an “equals” sign

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

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

Publisher: PEARSON

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Chapter 3.1, Problem 38E

To determine

To sketch: The graph of the system of inequalities 6x−4y>8 and 2x+5y<5 .

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Chapter 3.1, Problem 37E

Chapter 3.1, Problem 39E

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Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 3.1 - Graph 3x + 2y 18.Ch. 3.1 - Graph the feasible region for the system...Ch. 3.1 - Prob. 1WE Ch. 3.1 - y=12x+1 Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E

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