I am a little confused everyone tells me that in a linear equation ax+by+c=0 where a and b are not equal to zero. But on the other hand there are e.g. which show 'a' as any real number, and c again as any real number but 'b' is 0. Can you explain why so??

Asked by  | 20th Oct, 2013, 12:58: PM

Expert Answer:

In the equation, we need at least one variable not equal to zero.
 
Suppose in the same example that you have mentioned, if a and b, both are equal to zero,
 
then the equation becomes, a x 0 +b x 0 + c =0
 
That is, the equation reduces to c = 0.
 
And if the constant is also zero, there is no point in defining the equation.
 
Take the example of 4 - 3x = 0
 
Here the coefficient b = 0 and hence 3x = 4, that is x = (4/3)
 
So in the number line it represents a point (4/3) and in the cartesian plane it represents a
 
line parallel to y-axis, and its equation is x = (4/3)
 
Suppose the equation is 4 - 3y = 0.
 
Here, a  = 0 and b = -3
 
Therefore, we have y  = (4/3)
 
Again in the number line it represents a point (4/3) and in the cartesian plane it represents a
 
line parallel to x-axis, and its equation is y = (4/3)
 
So for a linear equation either of the coefficients shoud be a non-zero real number.
 

Answered by Vimala Ramamurthy | 20th Oct, 2013, 01:42: PM

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