Answer
$(3,-4)$.
Work Step by Step
The first equation of the first line is
$\Rightarrow y=-x-1$
Plug $y=0$ for the $x-$intercept.
$\Rightarrow 0=-x-1$
Add $x$ to both sides.
$\Rightarrow 0+x=-x-1+x$
Simplify.
$\Rightarrow x=-1$
The $x-$intercept is $-1$, so the line passes through $(-1,0)$.
Plug $x=0$ for the $y-$intercept.
$\Rightarrow y=-(0)-1$
Simplify.
$\Rightarrow y=-1$
The $y-$intercept is $-1$, so the line passes through $(0,-1)$.
Checkpoint plug $x=1$.
$\Rightarrow y=-1-1$
Simplify.
$\Rightarrow y=-2$
The checkpoint is $(1,-2)$.
Draw a straight line through these the points $(-1,0)$ and $(0,-1)$ and notice that the point $(1,-2)$ is also on the line.
The second equation of the line is
$\Rightarrow 4x-3y=24$
Plug $y=0$ for the $x-$intercept.
$\Rightarrow 4x-3(0)=24$
$\Rightarrow 4x=24$
Divide both sides by $4$.
$\Rightarrow \frac{4x}{4}=\frac{24}{4}$
Simplify.
$\Rightarrow x=6$
The $x-$intercept is $6$, so the line passes through $(6,0)$.
Plug $x=0$ for the $y-$intercept.
$\Rightarrow 4(0)-3y=24$
Simplify.
$\Rightarrow -3y=24$
Divide both sides by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{24}{-3}$
Simplify.
$\Rightarrow y=-8$
The $y-$intercept is $-8$, so the line passes through $(0,-8)$.
Checkpoint plug $x=3$.
$\Rightarrow 4(3)-3y=24$
Simplify.
$\Rightarrow 12-3y=24$
Subtract $12$ from both sides.
$\Rightarrow 12-3y-12=24-12$
Simplify.
$\Rightarrow -3y=12$
Divide both sides by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{12}{-3}$
Simplify.
$\Rightarrow y=-4$
The checkpoint is $(3,-4)$.
Draw a straight line through these the points $(6,0)$ and $(0,-8)$ and notice that the point $(3,-4)$ is also on the line.
We notice that the two graphs intersect at the point $(3,-4)$.
