System of First-Degree Equations in Two Variables

System of First-Degree Equations in Two Variables

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

Sys 2 Equa 2 Var

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

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

Numériser 1

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.

Sys 2 Equa 2 Var-B

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