#### Answer

The graph is shown below:

#### Work Step by Step

First we will replace the inequality sign with an equals sign.
Therefore,
$\begin{align}
& x+y=7 \\
& x+4y=-8
\end{align}$
Now we will graph these lines:
Consider $x+y=7$
For the $x$ -intercept set $y=0$ ,
Thus,
$\begin{align}
& x+0=7 \\
& x=7
\end{align}$
The line passes through $\left( 7,0 \right)$.
For the $y$ - intercept, put $x=0$ ,
Thus,
$\begin{align}
& 0+y=7 \\
& y=7
\end{align}$
The line passes through $\left( 0,7 \right)$.
Test that the statement is true or not by substituting $\left( 0,0 \right)$ in $x+y\le 7$ ,
$0+0\le 7$
Which is true.
Shade the half plane containing the points.
Consider $x+4y=-8$
For the $x$-intercept, put $y=0$ ,
$\begin{align}
& x+4\times 0=-8 \\
& x=-8
\end{align}$
The line passes through $\left( -8,0 \right)$.
For the $y$ - intercept, put $x=0$ ,
Thus,
$\begin{align}
& 0+4y=-8 \\
& 4y=-8 \\
& y=\frac{-8}{4} \\
& =-2
\end{align}$
The line passes through $\left( 0,-2 \right)$.
Test that the statement is true or not by substituting $\left( 0,0 \right)$ in $x+4y>-8$ ,
$0+0>-8\text{ false}$
Shade the half plane containing the points.
Plot the points $\left( -8,0 \right)$, $\left( 0,-2 \right)$ for the equation $x+y=7$ and the points $\left( 7,0 \right)$, $\left( 0,7 \right)$ for $x+4y=-8$
The graph of a solution of inequalities is plotted above.