Final answer:
Graphing the system of inequalities x−2y≤5, 3x+4y≥8, and y≤5 will yield a polygonal region on the Cartesian plane, which represents the set of all points that satisfy all three inequalities. The correct answer is C) The solution set forms a polygonal region.
Step-by-step explanation:
The system of inequalities presented includes three separate inequalities: x−2y≤5, 3x+4y≥8, and y≤5. To determine the solution set of this system, one must graph the inequalities on the Cartesian plane. Each inequality can be graphed as a half-plane. The intersection of these half-planes will represent the solution set.
When graphed, it's evident that the inequalities will form a region in the plane which is bounded and thus forms a polygonal region. So, the correct answer to the problem would be: C) The solution set forms a polygonal region. This region is the set of all points that satisfy all three inequalities simultaneously.
It's also important to note that in general, a system of linear inequalities will yield a solution set that could be an empty set, a region, or infinitely many solutions depending on the constraints imposed by the inequalities.
The correct answer is C.