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Equation solving. In mathematics, to solve an equation is to find its solutions, which are the values ( numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns.
The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
A parametric equation is an equation in which the solutions for the variables are expressed as functions of some other variables, called parameters appearing in the equations; A functional equation is an equation in which the unknowns are functions rather than simple quantities; Equations involving derivatives, integrals and finite differences:
Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. [ 1][ 2][ 3] Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining ...
Quadratic equation. In mathematics, a quadratic equation (from Latin quadratus ' square ') is an equation that can be rearranged in standard form as [ 1] where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.)
The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...
Closed-form expression. In mathematics, an expression or equation is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations ( +, −, ×, /, and integer powers) and function composition. Commonly, the allowed functions are n th root, exponential function, logarithm, and ...
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.