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:
\[\begin{align}
& x-y\le -1 \\
& 0-0\le -1 \\
& 0\le -1
\end{align}\]
The above inequality is not true. Thus, the region shaded is away from the origin for the inequality\[x-y\le -1\].
And,
\[\begin{align}
& x\ge 2 \\
& 0\ge 2 \\
\end{align}\]
The above inequality is not true. Thus, the region shaded is away from the origin for the inequality\[x\ge 2\].
Thus, graph of the system of linear inequalities, \[\begin{align}
& x-y\le -1 \\
& x\ge 2 \\
\end{align}\]is the common region of both the graphs and is shown below:
