Why can't A and B both be equal to zero in standard form of linear equation?

Question

Why can't A and B both be equal to zero in standard form of linear equation?

Answer 1

Standard form: ax+by=c

If A and B both are 0, you end up with 0=c. It's no longer a line, but just a definition of a constant. There's no more variables.

-IMP ;) :)  

Answer 2

Ax + By = C

if A and B = 0, you get...

0x + 0y = C

any number times 0 is 0

0 = C

If both A and B are both equal to zero, you don't have a linear equation, you have a tautology.  If you wanted to graph this, you would simply fill in the entire x,y plane.  Any two numbers would fulfil the equation.