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If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =
- a)– 2, 12/5
- b)– 1, 1/5
- c)– 6, 17/5
- d)6, – 12/5
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx –...
We can solve this system of equations by substitution.
From the second equation, we get x = -5/ky.
Substituting this into the first equation, we get:
2(-5/ky) + 3y + 5 = 0
Simplifying, we get:
-10/k + 3y + 5 = 0
3y = 10/k - 5
y = (10/k - 5)/3
Now, substituting x and y into the third equation, we get:
k(-5/ky) + (10/k - 5)/3 + 5 = 0
Simplifying, we get:
-5 + (10/k^2) - (5/3) + 5 = 0
10/k^2 = 5/3
k^2 = 6
k = ±√6
Therefore, the solutions are:
x = -5/(√6)y, y = (10/(√6) - 5)/3 for k = √6
x = -5/(-√6)y, y = (10/(-√6) - 5)/3 for k = -√6
From the second equation, we get x = -5/ky.
Substituting this into the first equation, we get:
2(-5/ky) + 3y + 5 = 0
Simplifying, we get:
-10/k + 3y + 5 = 0
3y = 10/k - 5
y = (10/k - 5)/3
Now, substituting x and y into the third equation, we get:
k(-5/ky) + (10/k - 5)/3 + 5 = 0
Simplifying, we get:
-5 + (10/k^2) - (5/3) + 5 = 0
10/k^2 = 5/3
k^2 = 6
k = ±√6
Therefore, the solutions are:
x = -5/(√6)y, y = (10/(√6) - 5)/3 for k = √6
x = -5/(-√6)y, y = (10/(-√6) - 5)/3 for k = -√6
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Question Description
If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer?.
If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the system of equations 2x + 3y + 5 = 0, x + ky + 5 = 0, kx – 12y – 14 = 0 be consistent, then k =a)– 2, 12/5b)– 1, 1/5c)– 6, 17/5d)6, – 12/5Correct answer is option 'C'. Can you explain this answer?.
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