Final Answer:
The solution set of a system of inequalities is the overlapping region where all inequalities are satisfied. Let's evaluate the points:
A) (-2,3): Does not satisfy the inequalities.
B) (-1,3): Satisfies the inequalities.
C) (0,0): Satisfies the inequalities.
D) (2,-2): Does not satisfy the inequalities.
Therefore, the correct options are B) (-1,3) and C) (0,0).
Explanation:
The correct options are B) (-1,3) and C) (0,0). The solution set for a system of inequalities represents the region where all individual inequalities overlap. Evaluating the provided points on a graph, we can determine which lie within this common area. Point A) (-2,3) doesn't satisfy the inequalities, as it falls outside the overlapping region. Point B) (-1,3) and Point C) (0,0), however, both satisfy the given inequalities. On the other hand, Point D) (2,-2) does not meet the criteria, lying outside the accepted region.
To elaborate, graphical representation involves shading the area where all inequalities overlap. Points within this shaded region are valid solutions. In this case, the graphical analysis reveals that only (-1,3) and (0,0) fall within the overlapping area, satisfying all given inequalities. Points outside this region do not meet the combined criteria of the system of inequalities.
Understanding the graphical representation of inequalities aids in visually identifying valid solutions to a system of inequalities, a fundamental concept in algebra and mathematics.