Jöfnurnar

Jöfnurnar is the Icelandic term for equations in mathematics. They are statements that assert the equality of two expressions, usually containing one or more variables. The aim of solving a jöfnu is to find values for the variables that make the equality true. Solutions can form a single value, a set of values, or, in the case of certain systems, a whole set of possibilities.

Types of jöfnur include simple linear equations, polynomial equations, and more complex forms such as rational, differential, or functional equations. A system of jöfnur consists of two or more equations that share common unknowns; a solution to the system is an assignment of values to the variables that satisfies every equation in the system simultaneously.

Solving methods vary with type. For linear jöfnur, algebraic manipulation, substitution, elimination, or matrix methods such as Gaussian elimination are common. Graphical interpretation treats a solution as the point where the graphs of the two sides intersect. For nonlinear or more advanced equations, techniques from algebra, calculus, and numerical analysis may be employed to obtain exact or approximate solutions.

Etymology and usage: the word derives from jafna meaning to balance or equalize, reflecting the idea of equality in an equation. Jöfnurnar are a foundational concept in algebra and are introduced early in mathematical education in Iceland and many other curricula.

Example: 2x + 3 = 7 has solution x = 2. A small system, x + y = 3 and 2x − y = 1, has solution x = 1, y = 2.