Question

are there more potential solutions to system of inequalities in a half plane or in the entire plane? why?

Answer 1

I have never thought about this question but found an interesting discussion of inequalities and half planes.

http://www.personal.kent.edu/~rmuhamma/Algorithms/MyAlgorithms/MathAlgor/linear.html

Answer 2

Every line ax + by = c divides the xy-plane into two regions called its half-planes.

•On one half-plane ax + by > c is true.
•On the other half-plane ax + by < c is true.
On the edge of the half-planes, ax + by = c is true.

I am tempted to say that the number of potential solutions is the same.

Read at the link above and see what you think.

@jackelyn_1234