egyenlete

An egyenlet is a mathematical statement that asserts the equality of two expressions, typically containing one or more unknowns. It is usually written with an equals sign. The values that satisfy the equation are called its solutions or roots. In Hungarian, egyenlet is the singular term; egyenletek is the plural.

Equations come in many forms. Linear equations have degree one and are solved by simple isolation of variables. Quadratic equations are degree two and are often solved by factoring, completing the square, or the quadratic formula. Polynomial equations generalize these to higher degrees. Exponential and logarithmic equations involve exponents or logarithms. Differential equations involve derivatives and describe rates of change. Systems of equations consist of two or more equations solved together, typically for a common set of unknowns. An identity is an equation that is true for all allowed values of the variable.

Solving an equation means finding all solutions within a given domain, such as the real numbers or the complex numbers. Methods depend on the type: isolating variables and applying inverse operations for simple cases; factoring, completing the square, or using the quadratic formula for polynomials; substitution and elimination for systems; and integration or special techniques for differential equations. Some equations have no solutions, others have a finite set of solutions, and identities have infinitely many solutions.

Equations are foundational in algebra and mathematics more broadly. They model relationships in science, engineering, economics, and everyday problem solving, providing a framework to determine unknown quantities from known data. In Hungarian usage, the term egyenlet captures this concept, with egyenletek as the plural form.