Simultaneously applied first-degree relationships of equality in two variables.
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.