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Two graphs of linear equations in two variables. In mathematics, a linear equation is an equation that may be put in the form + … + + =, where , …, are the variables (or unknowns), and ,, …, are the coefficients, which are often real numbers.
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. A solution is an assignment of ...
A linear system in three variables determines a collection of planes. The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1] [2] For example,
The blue line is the common solution to two of these equations. Linear algebra is the ... for solving simultaneous ... set of variables, for example, x 1, x 2 ...
[1] Elementary algebra, also known as high school algebra or college algebra, [2] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 3 ] whilst algebra introduces variables (quantities without fixed values).
An identity is an equation that is true for all possible values of the variable(s) it contains. Many identities are known in algebra and calculus. In the process of solving an equation, an identity is often used to simplify an equation, making it more easily solvable. In algebra, an example of an identity is the difference of two squares:
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 ...
In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to solve systems of polynomial equations.
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