Homework Help is Here – Start Your Trial Now!
Math
Algebra
Graph the solution to the following system of inequalities.

Graph the solution to the following system of inequalities.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question

Graph the solution to the following system of inequalities.

 

 

**Graphing Solutions to Systems of Inequalities** To effectively graph the solution to the given system of inequalities, follow these steps: 1. **Identify the inequalities:** - \( y > 2x - 5 \) - \( y \leq -5x + 2 \) 2. **Graph each inequality on the same coordinate plane:** **Graph \( y > 2x - 5 \):** - Start by graphing the boundary line \( y = 2x - 5 \). Since the inequality is strict (\( > \)), use a dashed line to represent that points on the line are not included in the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into \( y > 2x - 5 \): \( 0 > 2(0) - 5 \) simplifies to \( 0 > -5 \), which is true. - Shade the region above the dashed line, as this is the area where the inequality holds true. **Graph \( y \leq -5x + 2 \):** - Start by graphing the boundary line \( y = -5x + 2 \). Since the inequality is less than or equal to (\( \leq \)), use a solid line to indicate that points on the line are part of the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into \( y \leq -5x + 2 \): \( 0 \leq -5(0) + 2 \) simplifies to \( 0 \leq 2 \), which is true. - Shade the region below the solid line, as this is the area where the inequality holds true. 3. **Identify the solution region:** The solution to the system of inequalities is the region where the shaded areas overlap. This region satisfies both \( y > 2x - 5 \) and \( y \leq -5x + 2 \). **Understanding Graph Intersection:** Use the graph to determine the intersection of the shaded regions visually. Ensure to pay attention to whether the lines are dashed or solid to correctly
Transcribed Image Text:**Graphing Solutions to Systems of Inequalities** To effectively graph the solution to the given system of inequalities, follow these steps: 1. **Identify the inequalities:** - \( y > 2x - 5 \) - \( y \leq -5x + 2 \) 2. **Graph each inequality on the same coordinate plane:** **Graph \( y > 2x - 5 \):** - Start by graphing the boundary line \( y = 2x - 5 \). Since the inequality is strict (\( > \)), use a dashed line to represent that points on the line are not included in the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into \( y > 2x - 5 \): \( 0 > 2(0) - 5 \) simplifies to \( 0 > -5 \), which is true. - Shade the region above the dashed line, as this is the area where the inequality holds true. **Graph \( y \leq -5x + 2 \):** - Start by graphing the boundary line \( y = -5x + 2 \). Since the inequality is less than or equal to (\( \leq \)), use a solid line to indicate that points on the line are part of the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into \( y \leq -5x + 2 \): \( 0 \leq -5(0) + 2 \) simplifies to \( 0 \leq 2 \), which is true. - Shade the region below the solid line, as this is the area where the inequality holds true. 3. **Identify the solution region:** The solution to the system of inequalities is the region where the shaded areas overlap. This region satisfies both \( y > 2x - 5 \) and \( y \leq -5x + 2 \). **Understanding Graph Intersection:** Use the graph to determine the intersection of the shaded regions visually. Ensure to pay attention to whether the lines are dashed or solid to correctly
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Matrix Factorization
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS