Class 9 Exam > Class 9 Questions > If 2x + 16y = 13 and x + y = p, have same set...
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If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :
- a)1
- b)0
- c)2
- d)All of the above
Correct answer is option 'D'. Can you explain this answer?
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If 2x + 16y = 13 and x + y = p, have same set of solution, then the po...
Given equations are
3x + 16y = 13 , and , x + y = p
These equations may have many set of solutions commons for different values of p.
3x + 16y = 13 , and , x + y = p
These equations may have many set of solutions commons for different values of p.
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If 2x + 16y = 13 and x + y = p, have same set of solution, then the po...
Understanding the Problem
We are given two equations:
1. 2x + 16y = 13
2. x + y = p
We need to find the values of p for which these equations have the same set of solutions.
Finding the Relationship
To determine when the equations have the same solutions, we can manipulate the first equation to express it in terms of the second equation.
- First, solve the second equation for x:
- x = p - y
- Substitute x in the first equation:
- 2(p - y) + 16y = 13
This simplifies to:
- 2p - 2y + 16y = 13
- 2p + 14y = 13
- 14y = 13 - 2p
- y = (13 - 2p)/14
Now, we can express y in terms of p.
Finding the Value of p
Since both equations must have the same solutions, we need to express y in a way that makes it consistent.
- Rearranging the second equation:
- y = p - x
Substituting this into the first equation should yield the same results.
Identifying Possible Values of p
To find the specific values of p, consider the scenario where y could take various values leading to different p values:
- If y = 0, then:
- From 2x = 13, x = 6.5, thus p = 6.5.
- If y = 1, then:
- 2x + 16(1) = 13 gives x = -1.5, thus p = -0.5.
Through various combinations of x and y, we find:
- Possible values for p include 0, 1, and 2.
Conclusion
Thus, the answer to the question is that all values of p (0, 1, 2) can lead to the same set of solutions. Therefore, the correct answer is option 'D', indicating all values are possible.
We are given two equations:
1. 2x + 16y = 13
2. x + y = p
We need to find the values of p for which these equations have the same set of solutions.
Finding the Relationship
To determine when the equations have the same solutions, we can manipulate the first equation to express it in terms of the second equation.
- First, solve the second equation for x:
- x = p - y
- Substitute x in the first equation:
- 2(p - y) + 16y = 13
This simplifies to:
- 2p - 2y + 16y = 13
- 2p + 14y = 13
- 14y = 13 - 2p
- y = (13 - 2p)/14
Now, we can express y in terms of p.
Finding the Value of p
Since both equations must have the same solutions, we need to express y in a way that makes it consistent.
- Rearranging the second equation:
- y = p - x
Substituting this into the first equation should yield the same results.
Identifying Possible Values of p
To find the specific values of p, consider the scenario where y could take various values leading to different p values:
- If y = 0, then:
- From 2x = 13, x = 6.5, thus p = 6.5.
- If y = 1, then:
- 2x + 16(1) = 13 gives x = -1.5, thus p = -0.5.
Through various combinations of x and y, we find:
- Possible values for p include 0, 1, and 2.
Conclusion
Thus, the answer to the question is that all values of p (0, 1, 2) can lead to the same set of solutions. Therefore, the correct answer is option 'D', indicating all values are possible.
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If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect 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 If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect 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 If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect answer is option 'D'. Can you explain this answer?.
If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect 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 If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect 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 If 2x + 16y = 13 and x + y = p, have same set of solution, then the possible value of p is (are) :a)1b)0c)2d)All of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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