Question

How many solutions do the given simultaneous linear equations have? Evaluate using the graphical method.
$-x-y=1;$
$x+y+3=0$

Answer 1

Let's rewrite the equations in the intercept form.

$-x-y=1$
$\Rightarrow \frac{x}{-1}+\frac{y}{-1}=1$
$x-$intercept is $-1,$ and $y-$intercept is $-1.$

$x+y+3=0$
$\Rightarrow x+y=-3$
Dividing by $-3$ in both side.
$\Rightarrow \frac{x}{-3}+\frac{y}{-3}=1$
$x-$intercept is $-3,$ and $y-$intercept is $-3.$

The graph of the lines is as follows:

We find that both the lines are parallel, and there exist no point where they can meet.

Hence, they have no solution, i.e., zero solution.