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:
\[\begin{align}
& x+y<4 \\
& 0+0<4 \\
& 0<4
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[x+y<4\].
And,
\[\begin{align}
& 4x-2y<6 \\
& 4\left( 0 \right)-2\left( 0 \right)<6 \\
& 0-0<6 \\
& 0<6
\end{align}\]
The above inequality is true. Thus, the region shaded is towards the origin for the inequality\[4x-2y<6\].
Thus, the graph of the system of linear inequalities, \[\begin{align}
& x+y<4 \\
& 4x-2y<6 \\
\end{align}\]is the common region of both the graphs and is shown below:
