Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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Chapter 10.8, Problem 13WE
To determine

To plot: The graph of given pair of inequalities.

Expert Solution & Answer
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Answer to Problem 13WE

The graph of inequalities:

  x−y≥4x+y≤6

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 13WE , additional homework tip 1

Explanation of Solution

Given information:

  x−y≥4x+y≤6

Considering the first inequality: x−y≥4 .

This graph is a region on one of the side of line x−y=4 .

To determine the side of region, we will put a known point in inequality, if the point will satisfy the inequality, the inequality will lie on same side as of the known point,

If the known point will not satisfy the inequality, the region will lie on opposite side as of known point.

Taking known as (0,0) ,

  x−y≥40−0≥40≥4

As the point does not satisfies the inequality, required region lies on opposite side of line x−y=4 as of (0,0) .

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 13WE , additional homework tip 2

Considering the second inequality: x+y≤6 .

This graph is a region on one of the side of line x+y=6 .

To determine the side of region, we will put a known point in inequality, if the point will satisfy the inequality, the inequality will lie on same side as of the known point,

If the known point will not satisfy the inequality, the region will lie on opposite side as of known point.

Taking known as (0,0) ,

  x+y≤60+0≤60≤6

As the point satisfies the inequality, required region lies on same side of line x+y=6 as of (0,0) .

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 13WE , additional homework tip 3

Combining the region of both inequality, we get

  Algebra: Structure And Method, Book 1, Chapter 10.8, Problem 13WE , additional homework tip 4

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Chapter 10.8, Problem 12WE
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Chapter 10.8, Problem 14WE

Chapter 10 Solutions

Algebra: Structure And Method, Book 1

Ch. 10.1 - Prob. 1OECh. 10.1 - Prob. 2OECh. 10.1 - Prob. 3OECh. 10.1 - Prob. 4OECh. 10.1 - Prob. 5OECh. 10.1 - Prob. 6OECh. 10.1 - Prob. 7OECh. 10.1 - Prob. 8OECh. 10.1 - Prob. 9OECh. 10.1 - Prob. 10OE
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UG/ linear equation in linear algebra; Author: The Gate Academy;https://www.youtube.com/watch?v=aN5ezoOXX5A;License: Standard YouTube License, CC-BY
System of Linear Equations-I; Author: IIT Roorkee July 2018;https://www.youtube.com/watch?v=HOXWRNuH3BE;License: Standard YouTube License, CC-BY