Question
Sat September 29, 2012 By: Kartik
I came across a question which went like this:

When do we say that a linear equation with two variables vanishes?

Expert Reply
Sat September 29, 2012

8xy ? 12y + 2x – 3 = 4y (2x – 3) + 1 (2x – 3) = (2x – 3) (4y + 1)

 

The value(s) of x such that the expression 8xy ? 12y + 2x – 3 i.e. (2x – 3) (4y + 1) vanishes for all values of y, means it is required to find the value(s) of x such that the value of the equation (2x – 3) (4y + 1) will be zero irrespective of y (independent of y or for any value of y).

For any value of y, (4y + 1) may or may not be equal to zero.

Since, (2x – 3) (4y + 1) = 0 and (4y + 1) may or may not be equal to zero so, (2x – 3) = 0

i.e. x = 3

Or, x = 3/2

 

The correct answer is D.

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