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The system of equations x - 4y = 8, 3x - 12y = 24
a. has infinitely many solutions
b. may or may not have a solution
c. has no solution
d. has a unique solution?
a. has infinitely many solutions
b. may or may not have a solution
c. has no solution
d. has a unique solution?
Most Upvoted Answer
The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely ma...
Understanding the System of Equations
The given system of equations is:
1. x - 4y = 8
2. 3x - 12y = 24
To determine the nature of the solutions, we will analyze the equations.
Step 1: Simplifying the Equations
- The second equation, 3x - 12y = 24, can be simplified.
- Dividing the entire equation by 3 gives:
x - 4y = 8
Step 2: Identifying Relationship
- Now, we see that both equations are identical:
x - 4y = 8
x - 4y = 8
Conclusion: Infinitely Many Solutions
- Since both equations represent the same line, they intersect at infinitely many points.
- Therefore, the system does not provide a unique solution or a point of intersection.
Final Answer
- The system of equations has:
This is because both equations are essentially the same, confirming they represent the same linear relationship in a two-dimensional space.
The given system of equations is:
1. x - 4y = 8
2. 3x - 12y = 24
To determine the nature of the solutions, we will analyze the equations.
Step 1: Simplifying the Equations
- The second equation, 3x - 12y = 24, can be simplified.
- Dividing the entire equation by 3 gives:
x - 4y = 8
Step 2: Identifying Relationship
- Now, we see that both equations are identical:
x - 4y = 8
x - 4y = 8
Conclusion: Infinitely Many Solutions
- Since both equations represent the same line, they intersect at infinitely many points.
- Therefore, the system does not provide a unique solution or a point of intersection.
Final Answer
- The system of equations has:
- Infinitely many solutions
This is because both equations are essentially the same, confirming they represent the same linear relationship in a two-dimensional space.
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The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution?
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The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution?.
The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equations x - 4y = 8, 3x - 12y = 24 a. has infinitely many solutions b. may or may not have a solution c. has no solution d. has a unique solution?.
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