Answer
the solution set are the shaded areas
Work Step by Step
Using a table of values, the graph of
\begin{array}{l}\require{cancel}
2x+y=4
\\
y=-2x+4
,\end{array}
is determined (RED graph).
Using the testpoint, $
(0,0)
,$ then
\begin{array}{l}\require{cancel}
2x+y\le4
\\
2(0)+0\le4
\\
0+0\le4
\\
0\le4
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a $\text{
TRUE
}$ statement, then the testpoint is $\text{
INCLUDED
}$ in the area of the solution set.
The graph of $
y=2
$ is the horizontal line passing through $
(0,2)
.$ The graph of $
y\gt2
$ is the area above the graph of $
y=2
$ (BLUE graph).
A solid line is used for the symbols $\le$ and $\ge,$ while a dotted line is used for the symbols $\gt$ and $\lt.$
Since "or" is used, the solution set are the shaded areas.
