Questions: Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set. y ≥ 1/2 x + 2 y > -3/2 x - 2

To solve the system of inequalities graphically, we need to:

1. Plot the boundary lines for each inequality.
2. Determine the regions that satisfy each inequality.
3. Identify the overlapping region that satisfies both inequalities.
4. Choose a point within the overlapping region as a solution.

First, we need to graph the line \( y = \frac{1}{2} x + 2 \). This line has a slope of \( \frac{1}{2} \) and a y-intercept of 2.

1. Plot the y-intercept (0, 2).
2. Use the slope to find another point. From (0, 2), move up 1 unit and right 2 units to get the point (2, 3).
3. Draw the line through these points. Since the inequality is \( y \geq \frac{1}{2} x + 2 \), shade the region above the line.

Next, we graph the line \( y = -\frac{3}{2} x - 2 \). This line has a slope of \( -\frac{3}{2} \) and a y-intercept of -2.

1. Plot the y-intercept (0, -2).
2. Use the slope to find another point. From (0, -2), move down 3 units and right 2 units to get the point (2, -5).
3. Draw the line through these points. Since the inequality is \( y > -\frac{3}{2} x - 2 \), use a dashed line to indicate that points on the line are not included, and shade the region above the line.

To find the solution set, we need to identify the region where the shaded areas from both inequalities overlap.

1. The region above the line \( y \geq \frac{1}{2} x + 2 \) is shaded.
2. The region above the dashed line \( y > -\frac{3}{2} x - 2 \) is shaded.

The solution set is the area where these two shaded regions intersect.

To find a point in the solution set, we can choose any point within the overlapping shaded region. One such point is (0, 3).

\[ \boxed{(0, 3)} \]