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Equations

Which one of ...

Question

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equation has at least one solution, such that p + q + r $\neq$ 0?
x + 2y - 3z = p
2x + 5y - 11z = q
x - 2y + 7z = r

5p - 2q - r = 0

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5p + 2q + r = 0

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5q + 2q - r = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5q - 2q + r = 0

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Solution

The correct option is A 5p - 2q - r = 0
x + 2y - 3z = p ...(1)
2x + 5y - 11z = q ...(2)
x - 2y + 7z = r ...(3)
Going through the options, we find that 5 $\times$ (1) - 2 $\times$ (2) = (3)
Thus, equation in choice (a) is satisfied.

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