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:
\[\begin{align}
& 3x+6y\le 6 \\
& 3\left( 0 \right)+6\left( 0 \right)\le 6 \\
& 0+0\le 6 \\
& 0\le 6
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[3x+6y\le 6\].
And,
\[\begin{align}
& 2x+y\le 8 \\
& 2\left( 0 \right)+0\le 8 \\
& 0+0\le 8 \\
& 0\le 8 \\
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[2x+y\le 8\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& 3x+6y\le 6 \\
& 2x+y\le 8 \\
\end{align}\]is the common region of both the graphs and is shown:
