Class 10 Exam > Class 10 Questions > Q.10. Assertion (A): The value of k for which...
Start Learning for Free
Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}?
Most Upvoted Answer
Q.10. Assertion (A): The value of k for which the system of linear equ...
**Answer:**
**Assertion (A):** The value of k for which the system of linear equations kx + y = 2 and 6x - 2y = 3 has a unique solution is 3.
**Reason (R):** The graph of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 gives a pair of intersecting lines if a₁/a₂ = b₁/b₂.
To determine whether the given system of linear equations has a unique solution, we can solve the equations using any suitable method, such as substitution or elimination.
Let's solve the given system of equations using the method of elimination:
Equation 1: kx + y = 2
Equation 2: 6x - 2y = 3
To eliminate the y-variable, we can multiply Equation 1 by 2 and Equation 2 by 1:
2(kx + y) = 2(2) => 2kx + 2y = 4
1(6x - 2y) = 1(3) => 6x - 2y = 3
Now, we can add the two equations:
(2kx + 2y) + (6x - 2y) = 4 + 3
8kx + 0 = 7
8kx = 7
To have a unique solution, the coefficient of x should not be zero. Therefore, 8k ≠ 0, which implies k ≠ 0.
Now, we can solve for x:
8kx = 7
x = 7/(8k)
Since x is expressed in terms of k, the solution will be unique for all non-zero values of k.
Therefore, the value of k for which the system of linear equations has a unique solution is any non-zero value of k, not just 3.
**Conclusion:** The reason provided is incorrect. The graph of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 gives a pair of intersecting lines if a₁/a₂ = b₁/b₂ is satisfied. However, the reason does not explain why the value of k for a unique solution is 3. The correct reason is that the coefficient of x should not be zero (i.e., k ≠ 0) for a unique solution.
**Assertion (A):** The value of k for which the system of linear equations kx + y = 2 and 6x - 2y = 3 has a unique solution is 3.
**Reason (R):** The graph of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 gives a pair of intersecting lines if a₁/a₂ = b₁/b₂.
To determine whether the given system of linear equations has a unique solution, we can solve the equations using any suitable method, such as substitution or elimination.
Let's solve the given system of equations using the method of elimination:
Equation 1: kx + y = 2
Equation 2: 6x - 2y = 3
To eliminate the y-variable, we can multiply Equation 1 by 2 and Equation 2 by 1:
2(kx + y) = 2(2) => 2kx + 2y = 4
1(6x - 2y) = 1(3) => 6x - 2y = 3
Now, we can add the two equations:
(2kx + 2y) + (6x - 2y) = 4 + 3
8kx + 0 = 7
8kx = 7
To have a unique solution, the coefficient of x should not be zero. Therefore, 8k ≠ 0, which implies k ≠ 0.
Now, we can solve for x:
8kx = 7
x = 7/(8k)
Since x is expressed in terms of k, the solution will be unique for all non-zero values of k.
Therefore, the value of k for which the system of linear equations has a unique solution is any non-zero value of k, not just 3.
**Conclusion:** The reason provided is incorrect. The graph of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 gives a pair of intersecting lines if a₁/a₂ = b₁/b₂ is satisfied. However, the reason does not explain why the value of k for a unique solution is 3. The correct reason is that the coefficient of x should not be zero (i.e., k ≠ 0) for a unique solution.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}?
Question Description
Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? 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 Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}?.
Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? 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 Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}?.
Solutions for Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? defined & explained in the simplest way possible. Besides giving the explanation of
Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}?, a detailed solution for Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? has been provided alongside types of Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? theory, EduRev gives you an
ample number of questions to practice Q.10. Assertion (A): The value of k for which the system of linear equations kx y = 2 and 6x - 2y = 3 has a unique solution is 3. Reason (R): The graph of linear equations a_{1}*x b_{1}*y c_{1} = 0 and a_{2}*x b_{2}*y c_{2} = 0 gives a pair of intersecting lines if a_{1} / a_{2} = b_{1} / b_{2}? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup