Final answer:
In a system with two parallel linear inequality boundary lines, it is not possible to have a single point of solution, as parallel lines never meet. The possible scenarios are that the entire plane, a strip region, or no region at all could be the solution.
Step-by-step explanation:
When dealing with a system of two linear inequalities in two variables, if the boundary lines are parallel, the possibility of there being a single point of solution is not possible. Option B states there is a single point of solution, which cannot occur with parallel lines since parallel lines never intersect. We can have the following scenarios with two parallel boundary lines:
- A. The entire plane is a solution if both inequalities include all points on one side of each boundary line.
- C. There is a region with an infinite number of points of a solution if the inequalities include opposite sides of the parallel lines, creating a strip of solutions.
- D. There is no solution if the inequalities include the same sides of both lines, as there would be no overlap for a solution region.
Hence, the correct answer is B, 'There is a single point of solution' being not possible.