Answer
The graph is shown below:
Work Step by Step
Let us consider the inequalities $\begin{align}
& 2x-y\ge 4 \\
& x+2y<2 \\
\end{align}$
Substitute the equals symbol in place of the inequality and rewrite the equation as given below:
$\begin{align}
& 2x-y=4 \\
& x+2y=2 \\
\end{align}$
To find the value of the x-intercept, substitute y = 0 as given below:
$\begin{align}
& 2x-y=4 \\
& 2x-0=4 \\
& x=2
\end{align}$
Therefore, the coordinates of the line are $\left( 2,0 \right)$.
To find the value of the y-intercept, substitute x = 0 as given below:
$\begin{align}
& 2x-y=4 \\
& \left( 2\times 0 \right)-y=4 \\
& y=-4
\end{align}$
Therefore, the coordinates of the line are $\left( 0,-4 \right)$.
Consider the second equation: $ x+2y=2$,
To find the value of the x-intercept, substitute y = 0 as given below:
$\begin{align}
& x+2y=2 \\
& x+\left( 2\times 0 \right)=2 \\
& x=2
\end{align}$
Thus, the coordinates of the line are $\left( 2,0 \right)$.
To find the value of the y-intercept, substitute x = 0 as given below:
$\begin{align}
& x+2y=2 \\
& 0+2y=2 \\
& y=1
\end{align}$
Therefore, the coordinates of the line are $\left( 0,1 \right)$.
Then, take origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade:
$ 2x-y\ge 4\text{ and }x+2y<2$
$ 2*0-0\ge 4\text{ and }0+2*0<2$
$ 0\ge 4\text{ and }0<2$
So the origin is not included.
