Homework Help is Here – Start Your Trial Now!
Math
Algebra
Determine whether the following statement is true or false. If a system of two linear equations in two variables is consistent, it has exactly one solution. Choose the correct answer below. False True ...

Determine whether the following statement is true or false. If a system of two linear equations in two variables is consistent, it has exactly one solution. Choose the correct answer below. False True ...

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
**Statement Analysis: Linear Equation Systems** **Problem:** Determine whether the following statement is true or false. "If a system of two linear equations in two variables is consistent, it has exactly one solution." --- **Options:** - False - True **Explanation:** A consistent system of two linear equations in two variables can have: 1. **Exactly one solution** (intersecting lines). 2. **Infinitely many solutions** (coincident lines, meaning the equations represent the same line). Therefore, the statement "it has exactly one solution" is not always true. A consistent system can also have infinitely many solutions. Choose the correct answer based on this explanation.
Transcribed Image Text:**Statement Analysis: Linear Equation Systems** **Problem:** Determine whether the following statement is true or false. "If a system of two linear equations in two variables is consistent, it has exactly one solution." --- **Options:** - False - True **Explanation:** A consistent system of two linear equations in two variables can have: 1. **Exactly one solution** (intersecting lines). 2. **Infinitely many solutions** (coincident lines, meaning the equations represent the same line). Therefore, the statement "it has exactly one solution" is not always true. A consistent system can also have infinitely many solutions. Choose the correct answer based on this explanation.
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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