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:
\[\begin{align}
& x+y\le 4 \\
& 0+0\le 4 \\
& 0\le 4
\end{align}\]
As the above inequality is true. Thus, the region shaded is towards the origin for the inequality\[x+y\le 4\].
And,
\[\begin{align}
& y\ge 2x-4 \\
& 0\ge 2\left( 0 \right)-4 \\
& 0\ge -4
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[y\ge 2x-4\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& x+y\le 4 \\
& y\ge 2x-4 \\
\end{align}\]is the common region of both the graphs and is shown below:
