To analyze the system of linear inequalities from the graph, we need to determine the regions and boundaries defined by the inequalities and identify which points lie within the shaded solution region.

Steps:

1. Examine the boundaries:

   • There are two boundary lines: one solid line and one dashed line. The solid line indicates that the inequality includes the boundary (≤ or ≥), and the dashed line indicates the boundary is not included in the inequality (< or >).

2. Interpret the shading:

   • The solution region is shaded in the lower triangular area. This indicates the system of inequalities restricts the solution set to that region, which is below both lines.

Boundary Equations:

• The solid line appears to have a negative slope and can be written as:
  $y \leq -x + 2$ (since it crosses the y-axis at 2 and has a slope of -1).

• The dashed line appears to have a positive slope, and its equation can be written as:
  $y > \frac{1}{2}x - 4$ (it crosses the y-axis at -4 and has a slope of 0.5).

Shaded Region:

The shaded area is below the solid line $y \leq -x + 2$ and above the dashed line $y > \frac{1}{2}x - 4$.

Ordered Pairs:

To determine which ordered pairs are part of the solution set, we can test each point to see if it satisfies both inequalities.

Would you like to check specific ordered pairs or continue with this explanation? Let me know if you have any questions or want to delve deeper into any part of this analysis.

Here are 5 related questions for expansion:

1. How do you determine if a point lies in the solution region for a system of inequalities?
2. How does the slope of a line affect the solution set of an inequality?
3. What is the significance of solid and dashed boundary lines in graphing inequalities?
4. How can you determine the equation of a line from its graph?
5. What changes if the inequality symbol is flipped in one or both inequalities?

Tip: Always check if the boundary line is included (solid line) or excluded (dashed line) when determining which points satisfy the inequality.