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)
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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,...
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**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.
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