The coordinates of a point in the solution set are (2, 0).
To solve the system of inequalities graphically, we first need to graph each inequality individually.
Graphing y > -2x - 1
We can start by converting the inequality to slope-intercept form:
y > -2x - 1
y - (-2x - 1) > 0
y + 2x + 1 > 0
Now, we can graph the equation y + 2x + 1 = 0 as a blue line. Since the inequality is y > -2x - 1, we want to shade the region above the blue line.
Graphing y < 1/2x + 4
We can start by converting the inequality to slope-intercept form
y < 1/2x + 4
y - (1/2x + 4) < 0
y - 1/2x - 4 < 0
-2y + x + 8 < 0
Now, we can graph the equation -2y + x + 8 = 0 as a green line. Since the inequality is y < 1/2x + 4, we want to shade the region below the green line.
Solution Set:
The solution set to the system of inequalities is the region that is shaded both above the blue line and below the green line. This is shown in the following graph:
[Image of the graph with the shaded region]
One point in the solution set is (2, 0)