Properties

A system of first-degree equations in two variables generally has two equations. If the two equations are equivalent, the system is indeterminate; it has an infinite number of solutions:

• x + y = 16 and 3x + 3y = 48 are equivalent equations, and the two lines are coincident.

If the system has only one solution, then it is compatible and is called a Cramer's system.

• x + y = 16 and x – y = 8 are compatible equations and the two lines intersect at only one point.

If the system does not have a solution, then it is an incompatible system:

• x + y = 16 and x + y = 8 are incompatible equations, and the two lines are parallel.