Question

A linear equation in two variables $x$ and $y$ is of the form $ax+by+c=0$, where

• A. $a$$\ne$$0$, $b$$\ne$$0$
• B. $a$$\ne$$0$, $b$$=$$0$
• C. $a$$=$$0$, $b$$\ne$$0$
• D. $a=0,c=0$

Answer 1

The correct option is A

$a$$\ne$$0$, $b$$\ne$$0$

Explanation for the correct answer:

Option (A): $a$$\ne$$0$, $b$$\ne$$0$

An equation in the form $ax+by+c=0$ is a linear equation in two variables,

where $a,b$ and $c$ are real numbers.

such that $a$$\ne$$0$, $b$$\ne$$0$.

Explanation for incorrect solution:

option$\left(b\right)$ $a$$\ne$$0$, $b$$=$$0$ since $a,b$ and $c$ are real numbers $b$cannot be $0$.

option$\left(c\right)$$a$$=$$0$, $b$$\ne$$0$since $a,b$ and $c$ are real numbers $a$cannot be $0$.

option$\left(d\right)$$a=0,c=0$since $a,b$ and $c$ are real numbers $a,c$ cannot be $0$.

Hence, option (A) is the correct answer.