Answer
See below:
Work Step by Step
Substitute the coordinates of origin in the given system of inequalities and check whether the inequalities are true or not as:
\[\begin{align}
& 2x+y<4 \\
& 2\left( 0 \right)+0<4 \\
& 0+0<4 \\
& 0<4
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[2x+y<4\].
And,
\[\begin{align}
& x-y>4 \\
& 0-0>4 \\
& 0>4
\end{align}\]
The above inequality is not true. Thus, the region shaded is away from the origin for the inequality\[x-y>4\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& 2x+y<4 \\
& x-y>4 \\
\end{align}\]is the common region of both the graphs and is shown below:
