Final answer:
The student's task is to find which point is a solution to the system of inequalities y ≥ -x-3 and y ≥ 3x when graphed. Upon checking each point against both inequalities, it's found that none of the given points satisfy both inequalities, indicating there might be an error in the provided options or the inequalities.
Step-by-step explanation:
The student's question concerns finding a solution to a system of inequalities. The inequalities given are y ≥ -x-3 and y ≥ 3x. We need to find a point that satisfies both inequalities when graphed in the xy-plane.
To determine which of the given options is a solution, we can substitute the x and y values from each option into both inequalities:
- For (A) (-4, -2), substituting into both inequalities gives: -2 ≥ 4 - 3 (true) and -2 ≥ -12 (false).
- For (B) (-2, 0), substituting into both inequalities gives: 0 ≥ 2 - 3 (false) and 0 ≥ -6 (true).
- For (C) (0, -3), substituting into both inequalities gives: -3 ≥ 0 - 3 (true) and -3 ≥ 0 (false).
- For (D) (3, 4), substituting into both inequalities gives: 4 ≥ -3 - 3 (true) and 4 ≥ 9 (false).
The correct option must satisfy both inequalities. None of the points given satisfy both inequalities simultaneously, so there appears to be an error either in the question options or the system of inequalities provided, as none of the points provided are solutions to the system of inequalities.