Question

Please help me with these two Algebra problem. Thanks

Problem 1:
If two half planes never intersect, then their system of inequalities has no solution. True or False?

Problem 2:
If the boundary lines of two half planes are parallel, then they have no solution area. True or False?

Please answer as quick as possible and please answer as
Example:
True, because . . . .

Thanks again!!

Answer 1

Explanation:

First, a half plane can be defined as one side of a line, e.g. x < y-3.

1: True. A solution to two half planes is where the two half planes intersect. If they never intersect, then there literally cannot be a solution.

2: False. Take, for example, y=x and y=x+1. These two lines are parallel because in the equation y=mx+b, m represents the slope, and in these two lines, x is multiplied by 1, so both lines have the same slope and are therefore parallel. Then, take two boundary planes -- y > x and y>x+1. If we graph this out (see picture), the planes clearly intersect when y>x+1. The solution is where the planes intersect, so there is a solution area