Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3.4, Problem 39STP
To determine

To calculate: The solution set of the given inequalities by graphing.

  4x−3y<72y−x<−6

Expert Solution & Answer
Check Mark

Answer to Problem 39STP

The solution set of the inequalities 4x−3y<72y−x<−6 is,

  Algebra 2, Chapter 3.4, Problem 39STP , additional homework tip 1

Explanation of Solution

Given information:

The inequalities 4x−3y<72y−x<−6 .

Formula used:

To solve a system of inequalities by graphing, plot all the inequalities on the graph and shade the region that represents each inequality. The region that is common to all the inequalities i.e. shaded for all inequalities is the solution of the system.

Calculation:

Consider the given system of inequalities 4x−3y<72y−x<−6 .

Recall that to solve a system of inequalities by graphing, plot all the inequalities on the graph and shade the region that represents each inequality. The region that is common to all the inequalities i.e. shaded for all inequalities is the solution of the system.

To know whether the region will be shaded towards origin or away from the origin, substitute x=0 and y=0 in the inequality. If inequality holds true region will be shaded towards origin and if not away from the origin.

Now, substitute x=0 and y=0 in the inequality 4x−3y<7 and check whether it is true or not and then plot on the graph.

  4x−3y<74(0)−3(0)<70<7

Since, the inequality is true, so, its region will be shaded towards the origin as,

  Algebra 2, Chapter 3.4, Problem 39STP , additional homework tip 2

Now, substitute x=0 and y=0 in the inequality 2y−x<−6 and check whether it is true or not and then plot on the graph.

  2y−x<−62(0)−0<−60<−6

Since, the inequality is not true, so, its region will be shaded away from the origin as,

  Algebra 2, Chapter 3.4, Problem 39STP , additional homework tip 3

On combining both the inequalities on the graph, the common shaded region is unbounded region away from origin,

  Algebra 2, Chapter 3.4, Problem 39STP , additional homework tip 4

In the above figure, the color brown shaded region represents the solution set of the given system of inequalities.

Thus, the solution set of the inequalities 4x−3y<72y−x<−6 is,

  Algebra 2, Chapter 3.4, Problem 39STP , additional homework tip 5

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Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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