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# Linear equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. [1]

## Affine space

In mathematics, an affine space is a geometric structure that generalizes certain properties of parallel lines in Euclidean space.

## Algebraic equation

In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.

## Applied mathematics

Applied mathematics is a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry.

## Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

## Coefficient

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variables of the expression.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

## Consistent and inconsistent equations

In mathematics and in particular in algebra, a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the system&mdash;that is, that when substituted into each of the equations makes the equation hold true as an identity.

## Constant term

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.

## Coordinate system

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space.

## Determinant

In linear algebra, the determinant is a useful value that can be computed from the elements of a square matrix.

## Elementary algebra

Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics.

## Equation

In mathematics, an equation is an equality containing one or more variables.

## Equation solving

In mathematics, to solve an equation is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality).

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Extrapolation

In mathematics, extrapolation is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable.

## Field (mathematics)

In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.

## Gaussian elimination

In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.

## Graph of a function

In mathematics, the graph of a function f is the collection of all ordered pairs.

## Hyperplane

In geometry a hyperplane is a subspace of one dimension less than its ambient space.

## Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Linear algebra

Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces.

## Linear belief function

Linear Belief Function is an extension of the Dempster-Shafer theory of belief functions to the case when variables of interest are continuous.

## Linear equation over a ring

In algebra, linear equations and systems of linear equations over a field are widely studied.

## Linear inequality

In mathematics a linear inequality is an inequality which involves a linear function.

## Linear map

In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Nonlinear system

In physics and other sciences, a nonlinear system, in contrast to a linear system, is a system which does not satisfy the superposition principle – meaning that the output of a nonlinear system is not directly proportional to the input.

## Real number

In mathematics, a real number is a value that represents a quantity along a continuous line.

## Scalar (mathematics)

In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.

## Simultaneous equations

In mathematics, a set of simultaneous equations, also known as a system of equations, is a finite set of equations for which common solutions are sought.

## Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

## System of linear equations

In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.

## Tax bracket

Tax brackets are the divisions at which tax rates change in a progressive tax system (or an explicitly regressive tax system, although this is much rarer).

## Term (logic)

In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

## Three-dimensional space (mathematics)

Three-dimensional space (also: tri-dimensional space) is a geometric three-parameter model of the physical universe (without considering time) in which all known matter exists.

## Variable (mathematics)

In elementary mathematics, a variable is an alphabetic character representing a number, called the value of the variable, which is either arbitrary or not fully specified or unknown.

## Vertical line test

In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not.

## References

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