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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Solve the system of equations
![## Question 10
**Solve the system of equations.**
1. \(-x + 4y = -9\)
2. \(8x - 32y = 4\)
**Options:**
A. \((9, 0)\)
B. \((0, -9/4)\)
C. No solution
D. Infinitely many solutions
**Solution Explanation:**
To solve the system, let's first observe the given equations:
1. \(-x + 4y = -9\)
2. \(8x - 32y = 4\)
To check for consistency in the solutions, we can try to determine if the lines these equations represent are parallel, identical, or intersect at a single point.
Divide the entire second equation by 8 to make comparison easier:
\[ x - 4y = \frac{1}{2} \]
Now, rewrite both equations in the standard form for comparison:
1. \(-x + 4y = -9\) (Equation 1)
2. \(x - 4y = \frac{1}{2}\) (Equation 2, simplified)
Sum both equations:
\[ (-x + 4y) + (x - 4y) = -9 + \frac{1}{2} \]
This simplifies to:
\[ 0 = -\frac{17}{2} \]
Since the statement is false, the system of equations has **no solution**, which implies the lines are parallel.
Therefore, the correct answer is option:
C. No solution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28b27689-10ed-4307-b3bd-ec96e81b0de9%2F4100ce29-145a-451d-a690-f0ae8c4cf9e8%2Fscml1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Question 10
**Solve the system of equations.**
1. \(-x + 4y = -9\)
2. \(8x - 32y = 4\)
**Options:**
A. \((9, 0)\)
B. \((0, -9/4)\)
C. No solution
D. Infinitely many solutions
**Solution Explanation:**
To solve the system, let's first observe the given equations:
1. \(-x + 4y = -9\)
2. \(8x - 32y = 4\)
To check for consistency in the solutions, we can try to determine if the lines these equations represent are parallel, identical, or intersect at a single point.
Divide the entire second equation by 8 to make comparison easier:
\[ x - 4y = \frac{1}{2} \]
Now, rewrite both equations in the standard form for comparison:
1. \(-x + 4y = -9\) (Equation 1)
2. \(x - 4y = \frac{1}{2}\) (Equation 2, simplified)
Sum both equations:
\[ (-x + 4y) + (x - 4y) = -9 + \frac{1}{2} \]
This simplifies to:
\[ 0 = -\frac{17}{2} \]
Since the statement is false, the system of equations has **no solution**, which implies the lines are parallel.
Therefore, the correct answer is option:
C. No solution
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