/*! 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} Q. 393 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 393 (page 683)

In the following exercises, solve the following systems by graphing.

x鈭�y>鈭�2y鈮�3x+1

Short Answer

Expert verified

The solution is the area shaded twice which is the darker-shaded region.

Step by step solution

01

Step 1. Given Information 

In the given exercises we have to solve the following systems by graphing.

x鈭�y>鈭�2y鈮�3x+1
02

Step 2. Firstly graph the first equation.

Graph x鈭�y>鈭�2by graphing x鈭�y=鈭�2 and testing a point.

role="math" localid="1647879424631" x鈭�y=鈭�2Divideby鈭�2onbothsidex鈭�2鈭�y鈭�2=鈭�2鈭�2x鈭�2+y2=1

The intercepts are x=-2andy=2.

03

Step 3. Test (0,0). It makes the inequality true. So, shade the side that contains (0,0) red. 

04

Step 4. Now graph y≤3x+1 by graphing y=3x+1.

The slope m=3andb=1

Graph the second equation in the same rectangular coordinate system.

05

Step 5. Test (0,0). It makes the inequality true. So, shade the side that contains (0,0) blue.

06

Step 6. The point (0,0) is in the solution and we have already found it to be a solution of each inequality. 

The point of intersection of the two lines is included.

The solution is the area shaded twice which is the darker-shaded region.

07

Step 7. Now check the point on both equation.

x鈭�y=5x+2y=鈭�42-(-3)=52+2(-3)=-42+3=52-6=-45=5-4=-4

The solution set is

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

In the following exercises, translate to a system of equations and solve.

The difference of two complementary angles is 55 degrees. Find the measures of the angles.

In the following exercises, solve the systems of equations by substitution.

15x+4y=6-30x-8y=-12

Solve a System of Equations by Elimination -

5x-3y=-12x-y=2

Manny is making 12quarts of orange juice from concentrate and water. The number of quarts of water is 3times the number of quarts of concentrate. How many quarts of concentrate and how many quarts of water does Manny need?

Determine whether an ordered pair is a solution of a system of equations. In the following exercises, determine if the following points are solutions to the given system of equations.

2x+y=5x+y=1

(a)(4,-3)

(b)(2,0)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.