Explanation Given information: The system of inequalities is, { y ≥ − 2 x y ≤ 2 x y ≤ − 1 2 x + 2 The graph of the equations corresponding to the inequalities is shown in Figure 1.\ Graph: The given inequalities are, y ≥ − 2 x ...... (1) y ≤ 2 x ...... (2) y ≤ − 1 2 x + 2 ...... (3) The inequality (1) can be expressed in the form of equation as, y = − 2 x ...... (4) Consider the test points ( 1 , 1 ) and ( − 1 , − 1 ) to check whether the points satisfy the inequality (1). Substitute 1 for x and 1 for y in inequality (1) to check that the point ( 1 , 1 ) satisfy the inequality (1) as, 1 ≥ ? − 2 ( 1 ) 1 ≥ − 2 The point ( 1 , 1 ) is a part of the graph and lies above the line y = − 2 x . Substitute ( − 1 ) for x and ( − 1 ) for y in inequality (1) to check that the point ( − 1 , − 1 ) satisfy the inequality (1) as, − 1 ≥ ? − 2 ( − 1 ) − 1 ≥ 2 The point ( − 1 , − 1 ) is not a part of the graph and lies below the line y = − 2 x . The inequality (2) can be expressed in the form of equation as, y = 2 x ...... (5) Consider the test points ( 1 , 1 ) and ( − 1 , − 1 ) to check whether the points satisfy the inequality (2). Substitute 1 for x and 1 for y in inequality (2) to check that the point ( 1 , 1 ) satisfy the inequality (2) as, 1 ≤ ? 2 ⋅ 1 1 ≤ 2 The point ( 1 , 1 ) is a part of the graph and lies below the line y = 2 x . Substitute ( − 1 ) for x and ( − 1 ) for y in inequality (2) to check that the point ( − 1 , − 1 ) satisfy the inequality (2) as, − 1 ≤ ? 2 ( − 1 ) − 1 ≤ − 2 The point ( − 1 , − 1 ) is not a part of the graph and lies above the line y = 2 x . The inequality (2) can be expressed in the form of equation as, y = − 1 2 x + 2 ...... (6) Consider the test points ( 1 , 1 ) and ( − 1 , − 1 ) to check whether the points satisfy the inequality (2). Substitute 1 for x and 1 for y in inequality (3) to check that the point ( 1 , 1 ) satisfy the inequality (2) as, 1 ≤ ? − 1 2 ⋅ 1 + 2 1 ≤ ? − 1 + 4 2 1 ≤ 3 2 The point ( 1 , 1 ) is a part of the graph and lies below the line y = − 1 2 x + 2 . Substitute ( − 1 ) for x and ( − 1 ) for y in inequality (3) to check that the point ( − 1 , − 1 ) satisfy the inequality (3) as, − 1 ≤ ? − 1 2 ( − 1 ) + 2 − 1 ≤ ? 1 2 + 2 − 1 ≤ ? 1 + 4 2 − 1 ≤ 5 2 The point ( − 1 , − 1 ) is a part of the graph and lies below the line y = − 1 2 x + 2 . The vertices are obtained if the system of equations is solved. Add equation (4) and equation (5) to obtain the value of y as, 2 y = 0 y = 0 Substitute 0 for y in equation (4) to obtain the value of x as, 0 = − 2 x − 2 x = 0 x = 0 Therefore, the solution is the ordered pair ( 0 , 0 ) . Simplify equation (6) as, y = − x + 2 ⋅ 2 2 Simplify the above equation as, 2 y + x = 4 ...... (7) Multiply equation (5) by 2 as, 2 y − 4 x = 0 ...... (8) Subtract equation (7) from equation (8) to obtain the value of x is, x − ( − 4 x ) = 4 − 0 x + 4 x = 4 5 x = 4 x = 4 5 Substitute 4 5 for x in equation (5) to obtain the value of y as, y = 2 ⋅ 4 5 y = 8 5 Therefore, the solution is the ordered pair ( 4 5 , 8 5 )

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 5, Problem 50E

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The shaded region of the solution set of the system of inequalities {y≥−2xy≤2xy≤−12x+2.

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Chapter 5, Problem 49E

Chapter 5, Problem 51E

Chapter 5 Solutions

College Algebra

Ch. 5.1 - The system of equations {2x+3y=75xy=9} is a system...Ch. 5.1 - A system of equation in two variable can be solved...Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...Ch. 5.1 - Elimination method Use the elimination method to...

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To graph: The shaded region of the solution set of the system of inequalities { y ≥ − 2 x y ≤ 2 x y ≤ − 1 2 x + 2 .

Solution Summary: The graph of the equations corresponding to the inequalities is shown in Figure 1.

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To graph:

The shaded region of the solution set of the system of inequalities {y≥−2xy≤2xy≤−12x+2.

Want to see the full answer?

Chapter 5 Solutions

To graph: The shaded region of the solution set of the system of inequalities { y ≥ − 2 x y ≤ 2 x y ≤ − 1 2 x + 2 .

Solution Summary: The graph of the equations corresponding to the inequalities is shown in Figure 1.

Videos

To graph: The shaded region of the solution set of the system of inequalities {y≥−2xy≤2xy≤−12x+2.

Want to see the full answer?

Chapter 5 Solutions

To graph:

The shaded region of the solution set of the system of inequalities {y≥−2xy≤2xy≤−12x+2.