System of First-Degree Inequalities in Two Variables
Two simultaneously applied first-degree order relations in two variables constitute a system of first-degree inequalities in two variables.
Properties
If the two relations are equivalent, then the representation of the solution set is a half-plane.- Consider the following inequalities: x + y ≤ 2 and 3x + 3y ≤ 6; they represent the same inequality.
If the two relations are incompatible, then the solution set is ∅.
If the two relations are compatible, then the system has a non-empty solution set.
- Consider the following inequalities: x + y ≥ 0 and 2x + y ≤ 0; the representation of the solution set is the intersection of the two half-planes defined by the two inequalities.
