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One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can be
- a)– 10x – 14y + 4 = 0
- b)10x – 14y = – 4
- c)10x + 14y + 4 = 0
- d)– 10x + 14y + 4 = 0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
One equation of a pair of dependent linear equations is – 5x + 7...
If equation of a pair of dependent linear equations, then 
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1.
∴ the values would be
and c1 = 2×(−2)=−4
∴ the second equation can be 10x−14y = −4
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1.
∴ the values would be
and c1 = 2×(−2)=−4∴ the second equation can be 10x−14y = −4
Most Upvoted Answer
One equation of a pair of dependent linear equations is – 5x + 7...
Understanding Dependent Linear Equations
Dependent linear equations are those that represent the same line in a Cartesian plane. This means that one equation can be derived from the other by multiplying or dividing by a constant.
Given Equation
The given equation is:
-5x + 7y = 2
To find a dependent equation, we can multiply the entire equation by a non-zero constant.
Finding the Second Equation
Let's multiply the given equation by -2:
-2 * (-5x + 7y) = -2 * 2
This simplifies to:
10x - 14y = -4
Options to Evaluate
Now, let's analyze the options provided:
- Option A: -10x - 14y + 4 = 0
This rearranges to -10x - 14y = -4, which is not a dependent equation.
- Option B: 10x - 14y = -4
This is precisely what we derived from multiplying the original equation, confirming it is dependent.
- Option C: 10x + 14y + 4 = 0
This simplifies to 10x + 14y = -4, which is not equivalent.
- Option D: -10x + 14y + 4 = 0
This rearranges to -10x + 14y = -4, which is also not dependent.
Conclusion
Thus, the correct answer is:
- Option B: 10x - 14y = -4
This equation is a multiple of the original one, making it dependent and confirming that they represent the same line.
Dependent linear equations are those that represent the same line in a Cartesian plane. This means that one equation can be derived from the other by multiplying or dividing by a constant.
Given Equation
The given equation is:
-5x + 7y = 2
To find a dependent equation, we can multiply the entire equation by a non-zero constant.
Finding the Second Equation
Let's multiply the given equation by -2:
-2 * (-5x + 7y) = -2 * 2
This simplifies to:
10x - 14y = -4
Options to Evaluate
Now, let's analyze the options provided:
- Option A: -10x - 14y + 4 = 0
This rearranges to -10x - 14y = -4, which is not a dependent equation.
- Option B: 10x - 14y = -4
This is precisely what we derived from multiplying the original equation, confirming it is dependent.
- Option C: 10x + 14y + 4 = 0
This simplifies to 10x + 14y = -4, which is not equivalent.
- Option D: -10x + 14y + 4 = 0
This rearranges to -10x + 14y = -4, which is also not dependent.
Conclusion
Thus, the correct answer is:
- Option B: 10x - 14y = -4
This equation is a multiple of the original one, making it dependent and confirming that they represent the same line.
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Community Answer
One equation of a pair of dependent linear equations is – 5x + 7...
If equation of a pair of dependent linear equations, then
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1.
∴ the values would be and c1 = 2×(−2)=−4
∴ the second equation can be 10x−14y = −4
For satisfying the condition of dependent linear equations, the values of a2,b2 and c2 should be the multiples of the values of a1,b1 and c1.
∴ the values would be
and c1 = 2×(−2)=−4∴ the second equation can be 10x−14y = −4
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One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer?.
One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer?.
Solutions for One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer?, a detailed solution for One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can bea)– 10x – 14y + 4 = 0b)10x – 14y = – 4c)10x + 14y + 4 = 0d)– 10x + 14y + 4 = 0Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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