Final Answer:
The system of linear inequalities represented by the graph is y > -x + 3 and 3x - y > 2. Thus correct option is a.
Step-by-step explanation:
The graph displays two distinct inequalities. The first inequality, y > -x + 3, represents a boundary line where the region above the line is shaded. This line has a y-intercept of 3 and a slope of -1 (rise of -1 for every run of 1). The second inequality, 3x - y > 2, represents another boundary line with the shaded region above it. To determine the correct set of inequalities, we analyze the given options:
Option a) y > -x + 3 and 3x - y > 2:
Upon comparing the inequalities in option a) with the graph, both match the lines and shaded regions. The first inequality y > -x + 3 corresponds to the upper boundary line, and the second inequality 3x - y > 2 aligns with the lower boundary line. Therefore, option a) correctly represents the graph.
In the graph's context, the solution is the area where both shaded regions overlap, satisfying both inequalities simultaneously. The solution set for this system of inequalities is the region above the line y = -x + 3 and below the line 3x - y = 2. This area represents the valid solutions for the given inequalities when considered together.
Therefore, the correct is option a.