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

### 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 3*x*+ 3*y*= 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.