Answer
See below:
Work Step by Step
Consider the provided inequalities $\begin{align}
& x-2y\le 4 \\
& x\ge 2
\end{align}$
Consider each inequality once and choose some values for $ x $ and compute the value for $ y $, in order to form the ordered pairs which are used to plot the graph.
Consider, $ x-2y\le 4$
Choose some values of x and y satisfying $ x-2y=4$
So, put $ x=-1$ in the provided expression,
$\begin{align}
& -1-2y=4 \\
& -1-4=2y \\
& y=-\frac{5}{2} \\
& =-2.5
\end{align}$
Now, put $ x=0$,
$\begin{align}
& 0-2y=4 \\
& 2y=-4 \\
& y=-\frac{4}{2} \\
& =-2
\end{align}$
Now, put $ x=4$,
$\begin{align}
& 4-2y=4 \\
& 2y=0 \\
& y=0
\end{align}$
To check the region covered by $ x-2y\le 4$, substitute $\left( 0,0 \right)$ in the given equation. If $\left( 0,0 \right)$ satisfies the equation, then shade the region towards the origin.
Therefore substitute $\left( 0,0 \right)$ in $ x-2y\le 4$
$\begin{align}
& 0-2\left( 0 \right)\le 4 \\
& 0\le 4 \\
\end{align}$
