/*! 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 72 What is a solution of a system o... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 72

What is a solution of a system of linear inequalities?

Short Answer

Expert verified
The solution to a system of linear inequalities includes all ordered pairs that simultaneously satisfy all the inequalities in the system. We find this solution by determining the area of overlap, on a graph, of all individual inequalities in the system.

Step by step solution

01

Understanding a system of linear inequalities

A system of linear inequalities can be seen as an overlapping region on a graph where solutions to individual inequalities intersect. This region is often a segment, line, ray, or a general area on the graph.
02

Determining a solution

A solution to the system is any ordered pair (or sets of ordered pairs) that is in the overlapping region. In essence, this means that the pair of values for the variables in the ordered pair simultaneously satisfy all inequalities in the system. If there is no region of overlap, then the system of inequalities has no solution.
03

Understanding through an example

Assume a system of linear inequalities, \(y > 2x + 1\) and \(y < -x + 3\). The solution to this system is the set of all ordered pairs \((x, y)\) that satisfy both inequalities. Upon graphing these inequalities, one finds that the area of overlap is the region where \(y\) is greater than \(2x + 1\) and less than \(-x + 3\). All the ordered pairs of \((x, y)\) values in this region are solutions to the system.

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

Explain how to graph \(x-2 y<4\)

a. Solve: \(x-3<5\) b. Solve: \(2 x+4<14\) c. Give an example of a number that satisfies the inequality in part (a) and the inequality in part (b). d. Give an example of a number that satisfies the inequality in part (a), but not the inequality in part (b).

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I solved \(|x-2|=5\) by rewriting the equation as \(x-2=5\) or \(x+2=5\)

Explain how to solve a compound inequality involving or.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm considering the compound inequality \(x<8\) or \(x \geq 8\) so the solution set is \((-\infty, \infty)\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

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.