Egyenlet

Egyenlet (Hungarian for "equation") is a mathematical statement asserting the equality of two expressions, typically written with an equals sign (=) between a left-hand side and a right-hand side. An equation can contain constants, variables, functions and parameters; solving an equation means finding values of the variables that make the equality true.

Equations are classified by form and degree. Linear equations involve variables to the first power and have straightforward solution methods; polynomial equations include higher powers and may have multiple solutions; transcendental equations involve non-algebraic functions such as exponential, logarithmic or trigonometric expressions; differential equations relate functions and their derivatives and describe dynamical systems. Systems of equations consist of multiple simultaneous equations to be solved together.

Common solution techniques include algebraic manipulation, substitution, elimination, factoring, use of the quadratic formula, numerical approximation and analytic methods for differential equations. Existence and uniqueness theorems address when solutions exist and whether they are unique. Some equalities hold for all values of the variables (identities), while others are true only for particular values (conditional equations).

Equations are fundamental across mathematics, physics, engineering and economics, modeling relationships and constraints. They serve both as tools for computation and as conceptual frameworks for expressing laws, optimizing systems and predicting behavior. Historical developments in equation theory include the solving of polynomial equations and the formalization of algebraic structures that generalize equation-solving principles.