Determine if the following system has one solution, two solutions, no solution or infinitely many solutions. y = 12x + 1, y = -12x+1 A. one solution C. no solution D. infinitely many B. two solutions
Determine if the following system has one solution, two solutions, no solution or infinitely many solutions. y = 12x + 1, y = -12x+1 A. one solution C. no solution D. infinitely many B. two solutions
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**12. Determine if the following system has one solution, two solutions, no solution, or infinitely many solutions.**
\[ y = 12x + 1, \quad y = -12x + 1 \]
A. one solution B. two solutions C. no solution D. infinitely many
In the image, there are two linear equations provided in the form \( y = mx + b \). The potential answers (A, B, C, D) suggest determining the nature of solutions for the given system of equations, focusing specifically on one solution, two solutions, no solution, or infinitely many solutions. This requires recognizing if and where the two lines intersect.
**Explanation:**
These linear equations represent lines on a coordinate plane. To determine the number of solutions:
1. **Check Slopes and Y-Intercepts:**
- The equations are both in the form \( y = mx + b \).
- First equation: \( y = 12x + 1 \) (slope = 12, y-intercept = 1)
- Second equation: \( y = -12x + 1 \) (slope = -12, y-intercept = 1)
2. **Parallel Lines or Coinciding Lines:**
- Since the slopes are opposite (12 and -12) and the y-intercepts are the same (1), these lines are not parallel. Hence, they will intersect only once, as parallel lines would never intersect (no solution), and coinciding lines would have infinitely many solutions.
3. **Intersection Point:**
- To find the exact point of intersection, equate the two equations:
\[ 12x + 1 = -12x + 1 \]
Simplify this to:
\[ 24x = 0 \]
\[ x = 0 \]
- Substitute \( x = 0 \) back into either of the original equations:
\[ y = 12(0) + 1 = 1 \]
Thus, the intersection point is \( (0, 1) \).
Therefore, the system of equations has one solution.
**Correct Answer:**
A. one solution](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F076c3864-7786-4382-9dae-47b721ed5820%2F4112ac37-930e-4de4-86d1-d7b3c5f0043a%2F84c5g5_processed.png&w=3840&q=75)
Transcribed Image Text:**12. Determine if the following system has one solution, two solutions, no solution, or infinitely many solutions.**
\[ y = 12x + 1, \quad y = -12x + 1 \]
A. one solution B. two solutions C. no solution D. infinitely many
In the image, there are two linear equations provided in the form \( y = mx + b \). The potential answers (A, B, C, D) suggest determining the nature of solutions for the given system of equations, focusing specifically on one solution, two solutions, no solution, or infinitely many solutions. This requires recognizing if and where the two lines intersect.
**Explanation:**
These linear equations represent lines on a coordinate plane. To determine the number of solutions:
1. **Check Slopes and Y-Intercepts:**
- The equations are both in the form \( y = mx + b \).
- First equation: \( y = 12x + 1 \) (slope = 12, y-intercept = 1)
- Second equation: \( y = -12x + 1 \) (slope = -12, y-intercept = 1)
2. **Parallel Lines or Coinciding Lines:**
- Since the slopes are opposite (12 and -12) and the y-intercepts are the same (1), these lines are not parallel. Hence, they will intersect only once, as parallel lines would never intersect (no solution), and coinciding lines would have infinitely many solutions.
3. **Intersection Point:**
- To find the exact point of intersection, equate the two equations:
\[ 12x + 1 = -12x + 1 \]
Simplify this to:
\[ 24x = 0 \]
\[ x = 0 \]
- Substitute \( x = 0 \) back into either of the original equations:
\[ y = 12(0) + 1 = 1 \]
Thus, the intersection point is \( (0, 1) \).
Therefore, the system of equations has one solution.
**Correct Answer:**
A. one solution
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