Homework Help is Here – Start Your Trial Now!
Engineering
Computer Engineering
Solving system of linear inequalities in two unknowns Solve b) 3x + 2y >=6 2y + x < 8 Y<2 x,y >= 0 Find the region

Solving system of linear inequalities in two unknowns Solve b) 3x + 2y >=6 2y + x < 8 Y<2 x,y >= 0 Find the region

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
See similar textbooks
icon
Related questions
Question

Operations Research isn't math

## Solving System of Linear Inequalities in Two Unknowns ### Problem Statement Solve the following system of inequalities: 1. \( 3x + 2y \geq 6 \) 2. \( 2y + x < 8 \) 3. \( y < 2 \) 4. \( x, y \geq 0 \) ### Objective Find the region that satisfies all the given inequalities simultaneously. ### Steps to Solve 1. **Graph the inequalities on a coordinate plane:** - For \( 3x + 2y \geq 6 \): - Convert the inequality to the boundary line equation \( 3x + 2y = 6 \). - Find the intercepts. When \( x = 0 \), \( y = 3 \); when \( y = 0 \), \( x = 2 \). - Draw the boundary line and shade the region above it, since \( 3x + 2y \geq 6 \). - For \( 2y + x < 8 \): - Convert the inequality to the boundary line equation \( 2y + x = 8 \). - Find the intercepts. When \( x = 0 \), \( y = 4 \); when \( y = 0 \), \( x = 8 \. - Draw the boundary line and shade the region below it, since \( 2y + x \lt 8 \). - For \( y < 2 \): - Draw a horizontal line at \( y = 2 \) and shade below this line. - For \( x, y \geq 0 \): - Shade the region in the first quadrant (where both \( x \) and \( y \) are non-negative). 2. **Identify the overlapping region:** - The solution region is where all the above shaded regions overlap on the coordinate plane. By finding the common area, you will identify the region that satisfies all the inequalities. This region represents the solution to the system of linear inequalities. ### Conclusion By graphically representing each inequality and determining the intersecting region, you can find the solution to the system of linear inequalities. This method is useful for visualizing and solving multi-variable inequalities.
Transcribed Image Text:## Solving System of Linear Inequalities in Two Unknowns ### Problem Statement Solve the following system of inequalities: 1. \( 3x + 2y \geq 6 \) 2. \( 2y + x < 8 \) 3. \( y < 2 \) 4. \( x, y \geq 0 \) ### Objective Find the region that satisfies all the given inequalities simultaneously. ### Steps to Solve 1. **Graph the inequalities on a coordinate plane:** - For \( 3x + 2y \geq 6 \): - Convert the inequality to the boundary line equation \( 3x + 2y = 6 \). - Find the intercepts. When \( x = 0 \), \( y = 3 \); when \( y = 0 \), \( x = 2 \). - Draw the boundary line and shade the region above it, since \( 3x + 2y \geq 6 \). - For \( 2y + x < 8 \): - Convert the inequality to the boundary line equation \( 2y + x = 8 \). - Find the intercepts. When \( x = 0 \), \( y = 4 \); when \( y = 0 \), \( x = 8 \. - Draw the boundary line and shade the region below it, since \( 2y + x \lt 8 \). - For \( y < 2 \): - Draw a horizontal line at \( y = 2 \) and shade below this line. - For \( x, y \geq 0 \): - Shade the region in the first quadrant (where both \( x \) and \( y \) are non-negative). 2. **Identify the overlapping region:** - The solution region is where all the above shaded regions overlap on the coordinate plane. By finding the common area, you will identify the region that satisfies all the inequalities. This region represents the solution to the system of linear inequalities. ### Conclusion By graphically representing each inequality and determining the intersecting region, you can find the solution to the system of linear inequalities. This method is useful for visualizing and solving multi-variable inequalities.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Computer Networking: A Top-Down Approach (7th Edi…
Computer Networking: A Top-Down Approach (7th Edi…
Computer Engineering
ISBN:
9780133594140
Author:
James Kurose, Keith Ross
Publisher:
PEARSON
Computer Organization and Design MIPS Edition, Fi…
Computer Organization and Design MIPS Edition, Fi…
Computer Engineering
ISBN:
9780124077263
Author:
David A. Patterson, John L. Hennessy
Publisher:
Elsevier Science
Network+ Guide to Networks (MindTap Course List)
Network+ Guide to Networks (MindTap Course List)
Computer Engineering
ISBN:
9781337569330
Author:
Jill West, Tamara Dean, Jean Andrews
Publisher:
Cengage Learning
Concepts of Database Management
Concepts of Database Management
Computer Engineering
ISBN:
9781337093422
Author:
Joy L. Starks, Philip J. Pratt, Mary Z. Last
Publisher:
Cengage Learning
Prelude to Programming
Prelude to Programming
Computer Engineering
ISBN:
9780133750423
Author:
VENIT, Stewart
Publisher:
Pearson Education
Sc Business Data Communications and Networking, T…
Sc Business Data Communications and Networking, T…
Computer Engineering
ISBN:
9781119368830
Author:
FITZGERALD
Publisher:
WILEY
SEE MORE TEXTBOOKS