The Solution:
Given the system of inequalities below:
[tex]\begin{gathered} x>4 \\ y\ge-6 \end{gathered}[/tex]
Graphing the inequalities, we have:
To choose the type of boundary line for the inequalities.
[tex]Dashed\text{ \lparen....\rparen for x>4}[/tex][tex]\text{ Solid \lparen-\rparen for y}\ge-6[/tex]
Enter two points on the boundary line.
For the inequality x>4:
[tex]\begin{gathered} \left(4,-6\right)\text{ and} \\ \lparen10,-6) \end{gathered}[/tex]
For the second inequality, two points on the boundary line are:
[tex]\begin{gathered} \left(4,-6\right)\text{ and} \\ \left(4,0\right? \end{gathered}[/tex]
The region to be shaded is region B as shown in my graph above (though I do not know how A and B are labeled in the given graph)