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,...
Related questions
Question
![**Problem: Solve by elimination.**
Given the system of equations:
1. \(5x - 2y = 3\)
2. \(15x - 6y = 9\)
**Options:**
- \((2, 2)\)
- \((1, 1)\)
- Infinite solutions
- \((-2, -2)\)
To solve by elimination:
First, observe that the second equation \(15x - 6y = 9\) is a multiple of the first equation \(5x - 2y = 3\). Multiplying the first equation by 3 results in:
\[
3(5x - 2y) = 3 \times 3
\]
This gives:
\[
15x - 6y = 9
\]
The two equations are identical, meaning they represent the same line. Thus, they have infinite solutions. Both equations express the same linear relation, which means every point on the line is a solution. Therefore, the correct answer is "Infinite solutions."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5feef8a3-4722-4969-8d03-b0e4b16fec00%2Fead2bd84-c21f-455f-abc7-dce0b95a61fe%2Fxhbzqus_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Solve by elimination.**
Given the system of equations:
1. \(5x - 2y = 3\)
2. \(15x - 6y = 9\)
**Options:**
- \((2, 2)\)
- \((1, 1)\)
- Infinite solutions
- \((-2, -2)\)
To solve by elimination:
First, observe that the second equation \(15x - 6y = 9\) is a multiple of the first equation \(5x - 2y = 3\). Multiplying the first equation by 3 results in:
\[
3(5x - 2y) = 3 \times 3
\]
This gives:
\[
15x - 6y = 9
\]
The two equations are identical, meaning they represent the same line. Thus, they have infinite solutions. Both equations express the same linear relation, which means every point on the line is a solution. Therefore, the correct answer is "Infinite solutions."
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