Final Answer:
The solution to the system of inequalities X + Y ≤ -1 and X + Y ≥ 3 is the empty set (∅).
Step-by-step explanation:
To determine the solution to the system of inequalities, we analyze the intersection of their solution regions. For the first inequality X + Y ≤ -1, we can rearrange it to Y ≤ -X - 1, indicating that the solution lies below the line Y = -X - 1.
Similarly, for the second inequality X + Y ≥ 3, rearranging gives Y ≥ -X + 3, representing the solution above the line Y = -X + 3.
Graphically, the two lines have different slopes, and their intersection forms a region that does not overlap. Therefore, there is no common area where both inequalities are satisfied, resulting in an empty set as the solution. This implies that there are no values of X and Y that simultaneously satisfy both inequalities. The solution to the system is denoted by the empty set symbol (∅), indicating an inconsistent system without a feasible solution.