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:
\[\begin{align}
& 2x-y<3 \\
& 2\left( 0 \right)-0<3 \\
& 0+0<3 \\
& 0<3
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[2x-y<3\].
And,
\[\begin{align}
& x+y<6 \\
& 0+0<5 \\
& 0<6
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[x+y<6\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& 2x-y<3 \\
& x+y<6 \\
\end{align}\]is the common region of both the graphs and is shown below:
