Question

Can the solution to a system of two linear inequalities ever be “none”? Can it ever be a single point? Can there be an infinite number of solutions?

Answer 1

A) Yes

B) Yes

C) Yes

Explanation:

A) Yes, the solution to 2 linear inequalities can be none when the 2 lines representing the 2 inequalities on a graph are parallel to each other and thus would never intersect at a point.

B) Yes the solution to 2 linear inequalities can be a single point when the 2 lines representing the 2 inequalities on a graph intersect at a single point.

C) Yes the solution to 2 linear inequalities can be infinite number of solutions when the 2 lines representing the 2 inequalities on a graph overlap each other thereby making just a single line whereby all the coordinates of both inequalities intersect each other.