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Question

The equation x+2y+2z=1 and 2x+4y+4z=9 have


A

Only one solution

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B

Only two solutions

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C

Infinite number of solutions

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D

None of these

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Solution

The correct option is D

None of these


Explanation for the correct option

Given set of equations are x+2y+2z=1 and 2x+4y+4z=9

We know that, for a pair of equations of line a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2

  1. There is a unique solution if,
    a1a2≠b1b2 or c1c2≠b1b2 or a1a2≠c1c2
  2. There are infinite solutions if,
    a1a2=b1b2=c1c2=d1d2
  3. No solution if,
    a1a2=b1b2=c1c2≠d1d2

Here, a1=1, b1=2, c1=2, d1=1, a2=2, b2=4, c2=4 and d2=9

We observe that,
a1a2=b1b2=c1c2=12
And,
d1d2=19

So, a1a2=b1b2=c1c2≠d1d2

Therefore, there are no solutions.

Hence, option (D) i.e. None of these is correct.


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