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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.
Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'D'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
In case of assertion
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x – 2y = 8 ...(i)
5x – 10 = c ...(ii)
As a1/a2 = b1/b2 , so system of linear equations can never have unique solution.
∴ Assertion is incorrect.
In case of reason:
The equation of one line is 4x + 3y = 14.
We know that if two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are parallel, then
or
Hence, one of the possible, second parallel line is 12x + 9y = 5.
∴ Reason is correct Hence, assertion is incorrect but reason is correct.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion: For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.
Reason: Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
To determine the correctness of the assertion and the reason, let's analyze each statement individually.
Statement A: For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution to find the solution.
From the first equation, x - 2y = 8, we can rewrite it as x = 2y + 8.
Substituting this value of x into the second equation, we get 5(2y + 8) - 10y = c.
Simplifying further, we have 10y + 40 - 10y = c.
The y terms cancel out, and we're left with 40 = c.
Since the value of c is fixed at 40 for any real value, the second equation becomes 5x - 10y = 40.
Therefore, the system of equations x - 2y = 8 and 5x - 10y = c always has a unique solution, which is x = 2y + 8.
Statement R: Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
To determine if two lines are parallel, we need to compare their slopes. If the slopes are equal, the lines are parallel.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope.
Let's rewrite the given equations in slope-intercept form:
4x + 3y = 14
3y = -4x + 14
y = (-4/3)x + 14/3
12x + 9y = 5
9y = -12x + 5
y = (-12/9)x + 5/9
y = (-4/3)x + 5/9
Comparing the slopes of both equations, we can see that they are equal (-4/3).
Therefore, the given lines 4x + 3y = 14 and 12x + 9y = 5 are parallel.
Conclusion:
From the analysis above, we can conclude that both Assertion (A) and Reason (R) are true. However, Reason (R) does not provide the correct explanation for Assertion (A). The parallel lines mentioned in Reason (R) are not directly related to the given system of equations in Assertion (A).
Reason: Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
To determine the correctness of the assertion and the reason, let's analyze each statement individually.
Statement A: For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution to find the solution.
From the first equation, x - 2y = 8, we can rewrite it as x = 2y + 8.
Substituting this value of x into the second equation, we get 5(2y + 8) - 10y = c.
Simplifying further, we have 10y + 40 - 10y = c.
The y terms cancel out, and we're left with 40 = c.
Since the value of c is fixed at 40 for any real value, the second equation becomes 5x - 10y = 40.
Therefore, the system of equations x - 2y = 8 and 5x - 10y = c always has a unique solution, which is x = 2y + 8.
Statement R: Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.
To determine if two lines are parallel, we need to compare their slopes. If the slopes are equal, the lines are parallel.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope.
Let's rewrite the given equations in slope-intercept form:
4x + 3y = 14
3y = -4x + 14
y = (-4/3)x + 14/3
12x + 9y = 5
9y = -12x + 5
y = (-12/9)x + 5/9
y = (-4/3)x + 5/9
Comparing the slopes of both equations, we can see that they are equal (-4/3).
Therefore, the given lines 4x + 3y = 14 and 12x + 9y = 5 are parallel.
Conclusion:
From the analysis above, we can conclude that both Assertion (A) and Reason (R) are true. However, Reason (R) does not provide the correct explanation for Assertion (A). The parallel lines mentioned in Reason (R) are not directly related to the given system of equations in Assertion (A).
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution.Reason (R): Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14, 12x + 9y = 5.a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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