The graph above represents the solution to the system of inequalities:

1. $x - y < 7$ (dashed blue line, region above the line)
2. $x \geq 4$ (red vertical line, region to the right)
3. $2x + y \leq 4$ (solid green line, region below the line)

The shaded region where all the inequalities overlap represents the solution set for this system. This is the feasible area where all three conditions are satisfied.

Do you need further details or have any questions?

Here are 5 related questions to explore further:

1. How would the graph change if the inequality $x - y \leq 7$ were non-strict?
2. What happens if you change the inequality $x \geq 4$ to $x > 4$?
3. How would the solution change if one of the lines had a negative slope?
4. What is the intersection point between the lines $y = x - 7$ and $y = -2x + 4$?
5. Can you express the system as a linear programming problem and solve it?

Tip: When graphing inequalities, always pay attention to whether the inequality is strict (dashed line) or non-strict (solid line). This affects the boundaries of the solution set.