The graph in the image shows a triangular region bounded by three lines, and the shaded area represents the solution set to a system of inequalities. Let's break down the graph and corresponding inequalities:

1. Diagonal Line: The dashed diagonal line has a positive slope of 1 and crosses the origin (0, 0), so its equation is $y = x$. Since the shaded region is below the line, the inequality is $y < x$.

2. Vertical Line: There is a vertical dashed line at $x = 4$. The shaded region is to the left of this line, which corresponds to the inequality $x < 4$.

3. Horizontal Line: There is a horizontal dashed line at $y = 2$. The shaded region is above this line, so the inequality is $y > 2$.

Thus, the system of inequalities is: $\boxed{y < x, \, y > 2, \, x < 4}$ which matches option A.

Do you have any questions, or would you like further clarification on how the inequalities are derived?

Here are 5 related questions for further exploration:

1. How do we determine whether the inequality is $<$ or $>$ based on the shaded region?
2. Why does the inequality change from $y = x$ to $y < x$ in this context?
3. How would the graph look if we changed $y > 2$ to $y \geq 2$?
4. What would happen if one of the boundary lines were solid instead of dashed?
5. How do systems of inequalities relate to linear programming problems?

Tip: Always check whether the boundary line is solid or dashed—dashed means the line itself is not included in the solution!