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Consider the system of inequalities:

x−2y≤5
3x+4y≥8
y≤5
A) The solution set is an empty set.
B) The solution set is a single point.
C) The solution set forms a polygonal region.
D) The system has infinitely many solutions.

User NiXman
by
7.6k points

1 Answer

3 votes

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.

User William Xyz
by
7.8k points
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