linear equations - significado y definición. Qué es linear equations
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Qué (quién) es linear equations - definición

EQUATION THAT DOES NOT INVOLVE POWERS OR PRODUCTS OF VARIABLES
Linear equations; Point-slope; Point-slope formula; Point-slope equation; Point-slope form; Slope-intercept form; Y=mx+b; Slope intercept form; Y-y1=m(x-x1); Y = mx + b; Point slope form; Point slope formula; Y=x; Ax+By=C; Y=mx+c; Y-b=m(x-a); Linear equality; Linear Equation; Slope-intercept; Equation of a straight line; Equation of the straight line; Line equation; Intercept terms; First degree equation; First-degree equation; Point–slope form; Slope–intercept form; Y=b+mx; Ax+b=0; Linear constraint; Y line; Line Y; Equation of a line through 2 points
  • Two graphs of linear equations in two variables

System of linear equations         
  • The solution set for two equations in three variables is, in general, a line.
COLLECTION OF LINEAR EQUATIONS INVOLVING THE SAME SET OF VARIABLES
Linear simultaneous equations; Simultaneous linear equations; Homogeneous equation; Linear system of equations; Ax=b; Systems of linear equations; Homogeneous linear equation; Linear equation system; Vector equation; Ax=0; Linear Equation System; Algorithms for solving systems of linear equations; Solving systems of linear equations; Methods for solving systems of linear equations; Elimination of variables in systems of linear equations; Homogeneous system of linear algebraic equations; Homogeneous system of linear equations; Free variables (system of linear equations)
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
linear equation         
¦ noun an equation between two variables that gives a straight line when plotted on a graph.
Linear differential equation         
DIFFERENTIAL EQUATIONS THAT ARE LINEAR WITH RESPECT TO THE UNKNOWN FUNCTION AND ITS DERIVATIVES
Constant coefficients; Linear differential equations; General solution; Linear ordinary differential equation; First-order nonhomogeneous linear differential equation; First order linear differential equation; Linear ODE; Linear homogeneous differential equation; First-order linear differential equation; System of linear differential equations; Solution of a differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

Wikipedia

Linear equation

In mathematics, a linear equation is an equation that may be put in the form a 1 x 1 + + a n x n + b = 0 , {\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0,} where x 1 , , x n {\displaystyle x_{1},\ldots ,x_{n}} are the variables (or unknowns), and b , a 1 , , a n {\displaystyle b,a_{1},\ldots ,a_{n}} are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation, and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients a 1 , , a n {\displaystyle a_{1},\ldots ,a_{n}} are required to not all be zero.

Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.

The solutions of such an equation are the values that, when substituted for the unknowns, make the equality true.

In the case of just one variable, there is exactly one solution (provided that a 1 0 {\displaystyle a_{1}\neq 0} ). Often, the term linear equation refers implicitly to this particular case, in which the variable is sensibly called the unknown.

In the case of two variables, each solution may be interpreted as the Cartesian coordinates of a point of the Euclidean plane. The solutions of a linear equation form a line in the Euclidean plane, and, conversely, every line can be viewed as the set of all solutions of a linear equation in two variables. This is the origin of the term linear for describing this type of equations. More generally, the solutions of a linear equation in n variables form a hyperplane (a subspace of dimension n − 1) in the Euclidean space of dimension n.

Linear equations occur frequently in all mathematics and their applications in physics and engineering, partly because non-linear systems are often well approximated by linear equations.

This article considers the case of a single equation with coefficients from the field of real numbers, for which one studies the real solutions. All of its content applies to complex solutions and, more generally, for linear equations with coefficients and solutions in any field. For the case of several simultaneous linear equations, see system of linear equations.