/*! 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 65 Compare the graphs of \(3 x-2 y&... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 65

Compare the graphs of \(3 x-2 y>6\) and \(3 x-2 y \leq 6\). Discuss similarities and differences between the graphs.

Short Answer

Expert verified
The two inequalities \(3x - 2y > 6\) and \(3x - 2y \leq 6\) share the same line when graphed. However, \(3x - 2y > 6\) covers the area above the line (not including the line), while \(3x - 2y \leq 6\) includes the line and covers the area below the line.

Step by step solution

01

Graph the first inequality

Start by graphing the inequality \(3x - 2y > 6\). It can be helpful to first graph the line as if it was an equation by making it \(3x - 2y = 6\). The graph will be a straight line, where for every 2 units increase in y, there is a decrease of 3 units in x. The inequality portion implies that the area of the graph that satisfies this inequality is the one above the line.
02

Graph the second inequality

Next, graph the second inequality \(3x - 2y \leq 6\). Similar to the first case, start by graphing it as if it was an equation \(3x - 2y = 6\). Again, it's a straight line but this time the inequality indicates that the area of the graph satisfying this inequality is the area below or on the line.
03

Compare the two graphs

Having graphed both inequalities, it can now be observed that they both lie on the same line. The difference comes in the area they cover. The first inequality does not include the line and only covers the area above the line. The second inequality includes the line and the area below the line.

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

The law of supply and demand states that, in a free market economy, a commodity tends to be sold at its equilibrium price. At this price, the amount that the seller will supply is the same amount that the consumer will buy. Explain how systems of equations can be used to determine the equilibrium price.

What is a system of linear equations? Provide an example with your description.

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &3 x-4 y=x-y+4\\\ &2 x+6 y=5 y-4 \end{aligned} $$

At a price of \(p\) dollars per ticket, the number of tickets to a rock concert that can be sold is given by the demand model \(N=-25 p+7500 .\) At a price of \(p\) dollars per ticket, the number of tickets that the concert's promoters are willing to make available is given by the supply model \(N=5 p+6000\) a. How many tickets can be sold and supplied for \(\$ 40\) per ticket? b. Find the ticket price at which supply and demand are equal. At this price, how many tickets will be supplied and sold?

In Exercises \(19-30,\) solve each system by the addition method. \(2 x+3 y=6\) \(2 x-3 y=6\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

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.