Why can't a coefficient of x and y in standard form of a linear equation cannot both be zero?

Answer 1

Standard form of a linear equation is represented as

Ax + By = C

If A and B are the coefficients of the x and y and they are both equal to zero then C would always be equal to 0 for any given x and y value.

0x + 0y = 0

Since the linear equation is an equation between two variables that gives a straight line when plotted on a graph, (0,0) is a point itself and wouldn't be able to form a line.

Answer 2

In the standard form of a linear equation (Ax + By = C), both the coefficients of x and y cannot be zero simultaneously because this would result in a trivial equation where both variables are eliminated. If both coefficients were zero, the equation would reduce to 0 = C, which is not a valid linear equation. In order for the equation to represent a non-trivial line, at least one of the coefficients of x or y must be non-zero.

Answer 3

Oh, dude, it's like this: if both the coefficients of x and y were zero in a linear equation, you'd basically be left with just a big ol' zero on one side of the equation. And that's not really an equation at all, it's just... nothing. So, like, the equation wouldn't be able to represent a line in the xy-plane because, well, there wouldn't be a line to represent. So, it's kinda like trying to make a sandwich with no bread - you're just left with a sad pile of toppings.