Question

how many solution does a linear equation ax+by+c=0 has?

Answer 1

The linear equation $ax+by+c=0$ has infinitely many solutions.

Step-by-step explanation:

The given equation is $ax+by+c=0$

• This is a linear equation of two variables.
• It has infinitely many solutions.

We propose to find a few solutions using trial and error.

When $x=0$:

We consider $x=0$. Then,

$\quad by+c=0$

$\Rightarrow y=-\dfrac{c}{b}$

So, one solution is $\boxed{x=0,\:y=-\dfrac{c}{b}}$.

When $y=0$:

We consider $y=0$. Then,

$\quad ax+c=0$

$\Rightarrow x=-\dfrac{c}{a}$

So, one solution is $\boxed{x=-\dfrac{c}{a},\:y=0}$.

NOTE: In this way, we can find many other solutions and finally we can conclude that the given linear equation has infinitely many solutions.