/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 95 Explain how to graph the solutio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 95

Explain how to graph the solution set of a system of inequalities.

Short Answer

Expert verified
To graph the solution set of a system of inequalities, each inequality needs to be graphed individually by finding its line of equality and shading the region corresponding to the inequality sign. The solution set of the system is then found at the intersection of all the shaded regions, which represents the points satisfying all inequalities simultaneously.

Step by step solution

01

Understanding Basic Principles

The first step is to understand that the solution to a system of inequalities is the intersection of the solution sets of each inequality. It is the set of points that satisfy all inequalities at once. Also, when dealing with inequalities, it's important to keep the 'less than or equal to' format.
02

Graphing Each Inequality

Next, each inequality should be graphed separately. Start by temporarily looking at the inequality as an equality to draw a line. Then, depending on the inequality sign, shade the region either above or below that line. If the inequality is 'less than or equal to' or 'greater than or equal to', the line should be solid. If not, the line is dashed.
03

Finding the Solution Set

Lastly, the solution set is found at the intersection of the shaded regions of all inequalities. This is the area that satisfies all the inequalities at the same time. Highlighting this area on the graph identifies the possible solutions to the system of inequalities.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

write the partial fraction decomposition of each rational expression. $$ \frac{6 x-11}{(x-1)^{2}} $$

Describe a situation in your life in which you would really like to maximize something, but you are limited by at least two constraints. Can linear programming be used in this situation? Explain your answer.

How can you verify your result for the partial fraction decomposition for a given rational expression without using a graphing utility?

Find the partial fraction decomposition of $$ \frac{4 x^{2}+5 x-9}{x^{3}-6 x-9} $$

write the partial fraction decomposition of each rational expression. $$ \frac{4 x^{2}+3 x+14}{x^{3}-8} $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.