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 3*x*+ 3*y*≤ 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 2*x*+*y*≤ 0; the representation of the solution set is the intersection of the two half-planes defined by the two inequalities.