A system of linear inequalities is given.

Question

Which graph shows the solution to this system of inequalities?

A.
A system of linear inequalities with two solid lines is shown. The first solid line passes through the points (negative 4, negative 8), (2, 4), and (4, 8). The second solid line passes through the points (negative 8, 1), (4, 4) and (8, 5). A shaded common region is shown below the lines.

B.
A system of linear inequalities with two dashed lines is shown. The first dashed line passes through the points (negative 4, negative 8), (2, 4), and (4, 8). The second dashed line passes through the points (negative 8, 1), (4, 4) and (8, 5). A shaded common region is shown below the lines.

C.
A system of linear inequalities with two solid lines is shown. The first solid line passes through the points (negative 4, negative 8), (2, 4), and (4, 8). The second solid line passes through the points (negative 8, 1), (4, 4) and (8, 5). A shaded common region is shown above the lines.

D.
A system of linear inequalities with two dashed lines is shown. The first dashed line passes through the points (negative 4, negative 8), (2, 4), and (4, 8). The second dashed line passes through the points (negative 8, 1), (4, 4) and (8, 5). A shaded common region is shown above the lines.

Answer 1

To determine which graph represents the solution to the system of linear inequalities, we need to consider two key aspects:

1. Solid vs. Dashed Lines:

   • A solid line indicates that the points on the line are included in the solution (≤ or ≥ inequalities).
   • A dashed line indicates that the points on the line are not included in the solution (< or > inequalities).

2. Shaded Region:

   • The shaded region represents the set of points that satisfy the inequalities. If the inequality symbol is "less than" or "greater than," the shaded area will be below (for "<" or "≤") or above (for ">" or "≥") the respective line.

Without knowing the specific inequalities, I can give you guidance based on the descriptions:

• If the inequalities are strict (using < or >), the graphs with dashed lines (options B and D) are appropriate, and we need to check where the shaded region is located—above or below the lines.

• If the inequalities are inclusive (using ≤ or ≥), the graphs with solid lines (options A and C) are appropriate, and we need to again check the direction of the shaded region—above or below the lines.

Assuming you know whether the inequalities are strict or inclusive, check the line styles and the shaded regions to identify the correct graph. If you can specify the inequalities in your question, I would be able to provide a more precise answer.