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The value of k for which the system of equations 2x + ky = 12, x + 3y - 4 = 0 are inconsistent is
- a)21/4
- b)1/6
- c)6
- d)4/21
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The value of k for which the system of equations 2x + ky = 12, x + 3y ...
Given system of equations:
2x - ky = 12
x + 3y = 4
To check the consistency of the system, we can use any of the below methods:
- Graphical method
- Substitution method
- Elimination method
Let's solve the system of equations using the elimination method:
- Multiply the second equation by 2 and subtract it from the first equation
2x - ky = 12
-2x - 6y = -8
---------------------
(k-6)y = 4
Now, if (k-6) = 0, then the system will become inconsistent as we will get y = 0/0 which is undefined. Therefore, we need to find the value of k for which (k-6) is not equal to 0.
(k-6)y = 4
Dividing both sides by (k-6), we get:
y = 4/(k-6)
Now, since y is not equal to 0, we can substitute the value of y in the second equation and solve for x:
x + 3y = 4
x + 3(4/(k-6)) = 4
x = 4 - 12/(k-6)
x = (4(k-6) - 12)/(k-6)
x = (4k - 36)/(k-6)
Therefore, the system of equations is consistent for all values of k except k = 6. When k = 6, the system becomes inconsistent as y = 0/0.
Hence, the value of k for which the system of equations is inconsistent is 6. Therefore, option C is the correct answer.
2x - ky = 12
x + 3y = 4
To check the consistency of the system, we can use any of the below methods:
- Graphical method
- Substitution method
- Elimination method
Let's solve the system of equations using the elimination method:
- Multiply the second equation by 2 and subtract it from the first equation
2x - ky = 12
-2x - 6y = -8
---------------------
(k-6)y = 4
Now, if (k-6) = 0, then the system will become inconsistent as we will get y = 0/0 which is undefined. Therefore, we need to find the value of k for which (k-6) is not equal to 0.
(k-6)y = 4
Dividing both sides by (k-6), we get:
y = 4/(k-6)
Now, since y is not equal to 0, we can substitute the value of y in the second equation and solve for x:
x + 3y = 4
x + 3(4/(k-6)) = 4
x = 4 - 12/(k-6)
x = (4(k-6) - 12)/(k-6)
x = (4k - 36)/(k-6)
Therefore, the system of equations is consistent for all values of k except k = 6. When k = 6, the system becomes inconsistent as y = 0/0.
Hence, the value of k for which the system of equations is inconsistent is 6. Therefore, option C is the correct answer.
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Community Answer
The value of k for which the system of equations 2x + ky = 12, x + 3y ...
2x + ky = 12 , x +3y-4 = 0
2x + ky -12 = 0
here,
a1= 2 , b1 =k , c1 = (-12)
a2 = 1 , b2 = 3 , c2 =( -4)
since it has no solution..
so..
a1/ a2 = b1/b2 ≠ c1/c2
2/1 = k/3 ≠ 12/4
2/1 = k/3
2*3 = k
so.. k = 6
Get to know Important Definitions and Formulas of Pair of Linear Equations in two variables through the course:
2x + ky -12 = 0
here,
a1= 2 , b1 =k , c1 = (-12)
a2 = 1 , b2 = 3 , c2 =( -4)
since it has no solution..
so..
a1/ a2 = b1/b2 ≠ c1/c2
2/1 = k/3 ≠ 12/4
2/1 = k/3
2*3 = k
so.. k = 6
Get to know Important Definitions and Formulas of Pair of Linear Equations in two variables through the course:
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The value of k for which the system of equations 2x + ky = 12, x + 3y - 4 = 0 are inconsistent isa)21/4b)1/6c)6d)4/21Correct answer is option 'C'. 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 The value of k for which the system of equations 2x + ky = 12, x + 3y - 4 = 0 are inconsistent isa)21/4b)1/6c)6d)4/21Correct answer is option 'C'. 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 The value of k for which the system of equations 2x + ky = 12, x + 3y - 4 = 0 are inconsistent isa)21/4b)1/6c)6d)4/21Correct answer is option 'C'. Can you explain this answer?.
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