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:
\[\begin{align}
& x\ge 2 \\
& 0\ge 2 \\
\end{align}\]
The above in equation is not true. Thus, the region shaded is away from the origin for the inequality\[x\ge 2\].
And,
\[\begin{align}
& y\le 3 \\
& 0\le 3 \\
\end{align}\]
The above in equation is true. Thus, the region shaded is towards the origin for the inequality\[y\le 3\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& x\ge 2 \\
& y\le 3 \\
\end{align}\]is the common region of both the graphs and is shown below:
