Let's solve the system of inequalities graphically, as requested in the problem:

The system of inequalities is:

1. $x > 7$
2. $y \geq 3$

Interpretation:

• The inequality $x > 7$ means that we are considering all the points where the $x$-coordinate is greater than 7. In the graph, this is a vertical line at $x = 7$, and the region to the right of this line represents the solution set.
• The inequality $y \geq 3$ means that we are considering all points where the $y$-coordinate is greater than or equal to 3. In the graph, this is a horizontal line at $y = 3$, and the region above this line (including the line) is part of the solution.

Shaded Region:

• The region that satisfies both inequalities will be where both conditions are true. That is, $x$ is greater than 7 and $y$ is greater than or equal to 3.
• This corresponds to the upper-right quadrant of the graph beyond $x = 7$ and $y = 3$.

Answer:

Looking at the graph in your image, region D is the one in the upper-right area that satisfies both conditions.

So, the correct answer is D.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How would the graph change if $x \geq 7$ instead of $x > 7$?
2. What would the solution region look like if the inequalities were $x < 7$ and $y \leq 3$?
3. How would you represent a system of three inequalities graphically?
4. What if the inequality $y > 3$ had been a strict inequality (without the "equal to")?
5. How can we determine the vertices of the feasible region in a system of inequalities?

Tip: Always check if the inequalities include the boundary lines (i.e., whether the inequality is strict or includes "equal to") to shade the region correctly.