Question

In the equation $ax+by+c=0$, where c is a constant, if $a=b=0$ then

• A. None of these
• B. it is a linear equation in 2 variables
• C. it is a linear equation in 1 variable
• D. it is not a linear equation

Answer 1

The correct option is D

it is not a linear equation

Given equation: $ax+by+c=0$ where c is a constant

If $a=b=0$, then the equation reduces to c = 0 which is a constant. So, it will not be a linear equation.

Also, if either of a or b had been zero, it would have become a linear equation in one variable.
If a = 0, then equation will be by + c = 0.
Similarly, if b = 0, then equation will be ax + c = 0.
Now, by + c = 0 and ax + c = 0 are linear equations in one variable.

If both a $\ne$ 0 and b $\ne$ 0, then the given equation would have become a linear equation in two variables.