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Which one of the following conditions must p,q and r satisfy so that the following system of linear simultaneous
equations has atleast one solution, such that p + q + r = 0?
x + 2y – 3z = p ; 2x + 6y – 11z = q ; x – 2y + 7z = r
  • a)
    5p – 2q – r = 0
  • b)
    5p + 2q + r = 0
  • c)
    5p + 2q – r = 0
  • d)
    5p – 2q + r = 0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following conditions must p,q and r satisfy so that t...
It is given that p + q + r ≠ 0
Multiply the first equation by 5, second by -2 and third by -1, the coefficients of x, y and z all add up to zero.
5x + 10y - 15z = 5p
-4x - 12y + 22z = -2q
-x + 2y - 7z = -r
Adding all three equations:
5p - 2q - r = 0
The correct option is A.
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Most Upvoted Answer
Which one of the following conditions must p,q and r satisfy so that t...
To ensure that the given system of linear equations has at least one solution such that p + q + r = 0, the coefficients of x, y, and z in the equations should satisfy the condition that the sum of their coefficients in all three equations equals zero.

In other words, the condition is:

(1) 1p + 0q + 0r = 0
(2) 0p + 2q + 0r = 0
(3) 0p + 0q + 0r = 0

From equation (1), we can see that p must be equal to 0.

From equation (2), we can see that q must be equal to 0.

From equation (3), we can see that r can have any value since its coefficient is 0.

Therefore, the condition is p = 0, q = 0, and r can be any real number.
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Which one of the following conditions must p,q and r satisfy so that the following system of linear simultaneousequations has atleast one solution, such that p + q + r =0?x + 2y – 3z = p ; 2x + 6y – 11z = q ; x – 2y + 7z = ra)5p – 2q – r = 0b)5p + 2q + r = 0c)5p + 2q – r = 0d)5p – 2q + r = 0Correct answer is option 'A'. Can you explain this answer?
Question Description
Which one of the following conditions must p,q and r satisfy so that the following system of linear simultaneousequations has atleast one solution, such that p + q + r =0?x + 2y – 3z = p ; 2x + 6y – 11z = q ; x – 2y + 7z = ra)5p – 2q – r = 0b)5p + 2q + r = 0c)5p + 2q – r = 0d)5p – 2q + r = 0Correct answer is option 'A'. 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 Which one of the following conditions must p,q and r satisfy so that the following system of linear simultaneousequations has atleast one solution, such that p + q + r =0?x + 2y – 3z = p ; 2x + 6y – 11z = q ; x – 2y + 7z = ra)5p – 2q – r = 0b)5p + 2q + r = 0c)5p + 2q – r = 0d)5p – 2q + r = 0Correct answer is option 'A'. 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 Which one of the following conditions must p,q and r satisfy so that the following system of linear simultaneousequations has atleast one solution, such that p + q + r =0?x + 2y – 3z = p ; 2x + 6y – 11z = q ; x – 2y + 7z = ra)5p – 2q – r = 0b)5p + 2q + r = 0c)5p + 2q – r = 0d)5p – 2q + r = 0Correct answer is option 'A'. Can you explain this answer?.
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