Algebraic relations are said to be incompatible if they do not have any ordered pairs in common.

### Examples

- Two equations are incompatible if their solution sets are disjoints.

The equations*y*= 2*x*+ 1 and*y*= 2*x*+ 5 correspond to two parallel lines on a Cartesian plane. These lines do not have any points in common. The equations that represent them are incompatible relations (equations). - Two inequalities are incompatible if their solution sets are disjoint.

This is the case for the inequalities*y*< 2*x*+ 1 and*y*> 2*x*+ 5, because the half-planes that correspond to the solution sets of these inequalities are opposite.