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

Junaid Ayala 2022-02-18 Answered
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 a0,b0 and x,y are variables. (we often denote the condition a and b are not both zero by a2+b20.)"
I don’t understand this last condition.
How can we say that a2+b20 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
Answered 2022-02-19 Author has 7 answers
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
"a0,b0"
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Abbey Hope
Answered 2022-02-20 Author has 7 answers
Generally words "together", "both" and comma sign "," is used for logical operation AND (conjunction), denoted by xlandy. So
(a0,b0)(a0landb0)(a2+b20)
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