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:
\[\begin{align}
& 4x-5y\ge -20 \\
& 4\left( 0 \right)-5\left( 0 \right)\ge -20 \\
& 0-0\ge -20 \\
& 0\ge -20
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[4x-5y\ge -20\].
And,
\[\begin{align}
& x\ge -3 \\
& 0\ge -3 \\
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[x\ge -3\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& 4x-5y\ge -20 \\
& x\ge -3 \\
\end{align}\]is the common region of both the graphs and is shown below:
