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.