From a text book:

"The general form of a linear equation in two variables is$ax+by+c=0$ or, $ax+by=c$ where a,b,c are real numbers such that $a\ne 0,b\ne 0$ and x,y are variables.
(we often denote the condition a and b are not both zero by ${a}^{2}+{b}^{2}\ne 0$ .)"

I don’t understand this last condition.

How can we say that${a}^{2}+{b}^{2}\ne 0$ represents the condition that a and b are not both zero.

Let a=0,b=1, then also this condition fulfills.

"The general form of a linear equation in two variables is

I don’t understand this last condition.

How can we say that

Let a=0,b=1, then also this condition fulfills.