The system you've provided involves solving two linear inequalities graphically:

1. $x > 4$
2. $y \geq 2$

Steps for Solving Graphically:

• Inequality 1: $x > 4$ This represents a vertical line at $x = 4$. The region where $x > 4$ is to the right of this line.

• Inequality 2: $y \geq 2$ This represents a horizontal line at $y = 2$. The region where $y \geq 2$ is above this line.

The Overall Solution Set:

• The solution to this system is the intersection of these two regions: the area to the right of $x = 4$ and above $y = 2$. The intersection is the region where both conditions are satisfied simultaneously, meaning the area in the upper-right section of the graph (above the line $y = 2$ and to the right of $x = 4$).

Correct Answer:

You should select "the intersection of the individual solution sets" for shading.

Would you like further details or help with another part of this problem?

Here are 5 related questions you might find interesting:

1. How can we solve a system of linear inequalities involving different types of lines, such as vertical and horizontal?
2. How do you graph an inequality like $y < 3x + 1$ on a coordinate plane?
3. What is the difference between a system of equations and a system of inequalities graphically?
4. How do you shade regions for inequalities in a multi-variable system?
5. Can you explain how to solve inequalities involving quadratic functions graphically?

Tip: When graphing inequalities, always first plot the boundary line (or curve), then determine which side of the boundary should be shaded based on the inequality sign.