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≠0,b≠0 and x,y are variables. (we often denote the condition a and b are not both zero by a2+b2≠0.)" I don’t understand this last condition. How can we say that a2+b2≠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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From a text book:    &quot;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≠0,b≠0 and x,y are variables.  (we often denote the condition a and b are not both zero by a2+b2≠0.)&quot;    I don’t understand this last condition.    How can we say that a2+b2≠0 represents the condition that a and b are not both zero.    Let a=0,b=1, then also this condition fulfills.

paralovut91 · Accepted Answer

a and b are both zero ⇔ a=b=0, so    a and b are NOT both zero ⇔ at least one of a,b is not 0    which is equivalent to a2+b2=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 (a,b)≠(0,0) instead of    &quot;a≠0,b≠0&quot;

Abbey Hope · Accepted Answer

Generally words &quot;together&quot;, &quot;both&quot; and comma sign &quot;,&quot; is used for logical operation AND (conjunction), denoted by xlandy. So    (a≠0,b≠0)⇔(a≠0landb≠0)⇔(a2+b2≠0)

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

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