Final answer:
The solution to the system of inequalities lies in Quadrants 3 and 4.
Step-by-step explanation:
To graph the system of inequalities: y > -3 and y < -|x+2|, we need to graph the two individual inequalities.
The inequality y > -3 represents a horizontal line parallel to the x-axis at y = -3. Since y is greater than -3, the solution lies above this line, in the upper half of the coordinate plane.
The inequality y < -|x+2| represents a V-shaped graph opening downward. The vertex of the V is located at (-2, 0) and the V opens downwards because of the negative sign in front of the absolute value. Since y is less than -|x+2|, the solution lies below this V-shaped graph, in the lower half of the coordinate plane.
Therefore, the solution to the system of inequalities lies in Quadrants 3 and 4.