Final answer:
To find possible solutions to a system of linear inequalities, first graph the boundary lines, shade the solution regions, and then check if given points fall within the intersection of these regions by substituting the coordinates into the inequalities.
Step-by-step explanation:
The subject of this question is graphing and evaluating a system of linear inequalities to check for possible solutions. To graph the inequalities -2x + 6y > 24 and 5x + 2y < -16, we first convert them into equalities to find the boundary lines: -2x + 6y = 24 and 5x + 2y = -16. These lines are then graphed on a coordinate plane, and the appropriate regions representing the solutions for each inequality are shaded. The solution region for the system is the intersection of these shaded regions. To check if a given ordered pair is a solution, you substitute the values into the original inequalities.
To answer the question, we substitute the coordinates of each of the provided points A: (0, -8), B: (0, 0), C: (0, 4), and D: (10, 10) into the inequalities to verify which, if any, satisfy both conditions. For example, for point A (0, -8), the substitution gives -2(0) + 6(-8) = -48, which does not satisfy the first inequality -2x + 6y > 24, so point A is not a solution. The same process is repeated for the remaining points, thereby determining the correct answer.