# From a text book: "The general form of a linear equation in two variables is ax+by+c=0 o

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.
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paralovut91
a and b are both zero , so
a and b are NOT both zero $⇔$ at least one of a,b is not 0
which is equivalent to ${a}^{2}+{b}^{2}=0$ in the case that a,b are both real numbers.
Answering to your comment, yes, you are right. Maybe a better way to write in an inequality is $\left(a,b\right)\ne \left(0,0\right)$ instead of
"$a\ne 0,b\ne 0$"
###### Not exactly what you’re looking for?
Abbey Hope
Generally words "together", "both" and comma sign "," is used for logical operation AND (conjunction), denoted by $xl\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}y$. So
$\left(a\ne 0,b\ne 0\right)⇔\left(a\ne 0l\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}b\ne 0\right)⇔\left({a}^{2}+{b}^{2}\ne 0\right)$