To solve this problem, we need to match the shaded region in the graph to the correct system of inequalities from the options provided. Here’s the step-by-step process:

1. Analyze the Graph:

   • The shaded region is in the intersection of two constraints defined by lines.
   • One line has a negative slope and bounds the region from above, while the other line has a positive slope and bounds the region from below.

2. Examine the Equations:

   • The lines have the equations (likely): $y = -x + 6$ and $y = x - 1$.
   • The shaded region includes $y \leq -x + 6$ (area below the first line) and $y \geq x - 1$ (area above the second line).

3. Check the Options:

   • From the options:
     • $y \leq -x + 6$ and $y \geq x - 1$ correctly describe the graph's region. Thus, the corresponding choice is the correct system.

The correct answer is $y \leq -x + 6 \text{ AND } y \geq x - 1$.

Would you like me to explain how to derive the line equations from the graph? Here are some related questions and a tip for further exploration:

Related Questions:

1. How do we derive the slope-intercept form of a line from a graph?
2. What is the significance of the shaded region in a system of inequalities?
3. How do you graphically verify the solution to a system of inequalities?
4. What methods can be used to solve systems of inequalities algebraically?
5. How do boundary lines (solid or dashed) affect graphing inequalities?

Tip:

Always test a point (like the origin $(0, 0)$) to verify which region satisfies the inequality when analyzing systems of inequalities.