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