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,...
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![### System of Equations Multiple Choice Problem
Consider the following system of equations:
\[ x - y = 3 \]
\[ 2x^2 + 2y^2 = 10 \]
**Select all that apply.**
Choices:
A. \((-2, -1)\)
B. \((-1, -2)\)
C. \((1, -2)\)
D. \((2, -1)\)
E. \((2, 1)\)
F. There is no solution.
In this problem, you are asked to determine which of the given points satisfy both equations in the system. Each point should be tested to check if it satisfies the equations concurrently.
Highlighted choices (C and E) indicate the selected points that are presumed to verify the conditions provided by the equations.
### Explanation:
1. **Substituting Point \((-2, -1)\)**:
\[ x - y = -2 - (-1) = -2 + 1 = -1 \quad (\text{not equals to } 3) \]
\[ 2(-2)^2 + 2(-1)^2 = 8 + 2 = 10 \quad (\text{true}) \]
Since \(-2 - (-1) \neq 3\), the point \((-2, -1)\) does not satisfy the system.
2. **Substituting Point \((-1, -2)\)**:
\[ x - y = -1 - (-2) = -1 + 2 = 1 \quad (\text{not equals to } 3) \]
\[ 2(-1)^2 + 2(-2)^2 = 2 + 8 = 10 \quad (\text{true}) \]
Since \(-1 - (-2) \neq 3\), the point \((-1, -2)\) does not satisfy the system.
3. **Substituting Point \((1, -2)\)**:
\[ x - y = 1 - (-2) = 1 + 2 = 3 \quad (\text{true}) \]
\[ 2(1)^2 + 2(-2)^2 = 2 + 8 = 10 \quad (\text{true}) \]
Since \(1 - (-2) = 3\) and \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9926f15-7bb2-480a-811f-8f20f85d8688%2Fedcd228f-f888-4ef1-ab3c-8b36a8104f20%2Fu0u5iap_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### System of Equations Multiple Choice Problem
Consider the following system of equations:
\[ x - y = 3 \]
\[ 2x^2 + 2y^2 = 10 \]
**Select all that apply.**
Choices:
A. \((-2, -1)\)
B. \((-1, -2)\)
C. \((1, -2)\)
D. \((2, -1)\)
E. \((2, 1)\)
F. There is no solution.
In this problem, you are asked to determine which of the given points satisfy both equations in the system. Each point should be tested to check if it satisfies the equations concurrently.
Highlighted choices (C and E) indicate the selected points that are presumed to verify the conditions provided by the equations.
### Explanation:
1. **Substituting Point \((-2, -1)\)**:
\[ x - y = -2 - (-1) = -2 + 1 = -1 \quad (\text{not equals to } 3) \]
\[ 2(-2)^2 + 2(-1)^2 = 8 + 2 = 10 \quad (\text{true}) \]
Since \(-2 - (-1) \neq 3\), the point \((-2, -1)\) does not satisfy the system.
2. **Substituting Point \((-1, -2)\)**:
\[ x - y = -1 - (-2) = -1 + 2 = 1 \quad (\text{not equals to } 3) \]
\[ 2(-1)^2 + 2(-2)^2 = 2 + 8 = 10 \quad (\text{true}) \]
Since \(-1 - (-2) \neq 3\), the point \((-1, -2)\) does not satisfy the system.
3. **Substituting Point \((1, -2)\)**:
\[ x - y = 1 - (-2) = 1 + 2 = 3 \quad (\text{true}) \]
\[ 2(1)^2 + 2(-2)^2 = 2 + 8 = 10 \quad (\text{true}) \]
Since \(1 - (-2) = 3\) and \(
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