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The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 is
- a)(3, 4)
- b)(4, 3)
- c)(5, 3)
- d)The graphs will not intersect
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The point of intersection of graphs of the equations 3x + 4y = 12 and ...
Understanding the Equations
The two equations given are:
1. 3x + 4y = 12
2. 6x + 8y = 48
Analyzing the Second Equation
By simplifying the second equation, we can see if it is a multiple of the first:
- The second equation can be divided by 2:
- 6x + 8y = 48
- becomes: 3x + 4y = 24.
Comparing the Equations
Now, we compare the two simplified equations:
1. 3x + 4y = 12
2. 3x + 4y = 24
Determining Relationship
The left-hand sides of both equations are identical (3x + 4y), but the right sides are different (12 and 24). This indicates that:
- The two lines represented by these equations are parallel.
Conclusion: No Intersection
Since parallel lines never intersect, we conclude that:
- There is no solution to the system of equations.
- Therefore, the correct answer is option 'D': The graphs will not intersect.
Key Takeaways
- Parallel lines have the same slope but different y-intercepts.
- When two equations simplify to the same left-hand side but different right sides, they represent parallel lines.
This analysis shows why the answer to the intersection of the two graphs is that they do not intersect at any point.
The two equations given are:
1. 3x + 4y = 12
2. 6x + 8y = 48
Analyzing the Second Equation
By simplifying the second equation, we can see if it is a multiple of the first:
- The second equation can be divided by 2:
- 6x + 8y = 48
- becomes: 3x + 4y = 24.
Comparing the Equations
Now, we compare the two simplified equations:
1. 3x + 4y = 12
2. 3x + 4y = 24
Determining Relationship
The left-hand sides of both equations are identical (3x + 4y), but the right sides are different (12 and 24). This indicates that:
- The two lines represented by these equations are parallel.
Conclusion: No Intersection
Since parallel lines never intersect, we conclude that:
- There is no solution to the system of equations.
- Therefore, the correct answer is option 'D': The graphs will not intersect.
Key Takeaways
- Parallel lines have the same slope but different y-intercepts.
- When two equations simplify to the same left-hand side but different right sides, they represent parallel lines.
This analysis shows why the answer to the intersection of the two graphs is that they do not intersect at any point.
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Community Answer
The point of intersection of graphs of the equations 3x + 4y = 12 and ...
Let the point of intersection of lines be (a, b).
∴ 3α + 4b = 12 and
6α + 8b = 48
The above two equations have no solutions for (α, b)
∴ The graph will not intersect.
∴ 3α + 4b = 12 and
6α + 8b = 48
The above two equations have no solutions for (α, b)
∴ The graph will not intersect.
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The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer?.
The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point of intersection of graphs of the equations 3x + 4y = 12 and 6x + 8y = 48 isa)(3, 4)b)(4, 3)c)(5, 3)d)The graphs will not intersectCorrect answer is option 'D'. Can you explain this answer?.
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