 linear equation

Math.1. a firstorder equation involving two variables: its graph is a straight line in the Cartesian coordinate system.2. any equation such that the sum of two solutions is a solution, and a constant multiple of a solution is a solution. Cf. linear operator.[181020]
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statement that a firstdegree polynomial—that is, the sum of a set of terms, each of which is the product of a constant and the first power of a variable—is equal to a constant. Specifically, a linear equation in n variables is of the form a_{0} + a_{1}x_{1} + … + a_{n}x_{n} = c, in which x_{1}, …, x_{n} are variables, the coefficients a_{0}, …, a_{n} are constants, and c is a constant. If there is more than one variable, the equation may be linear in some variables and not in the others. Thus, the equation x + y = 3 is linear in both x and y, whereas x + y^{2} = 0 is linear in x but not in y. Any equation of two variables, linear in each, represents a straight line in Cartesian coordinates; if the constant term c = 0, the line passes through the origin.A set of equations that has a common solution is called a system of simultaneous equations. For example, in the systemboth equations are satisfied by the solution x = 2, y = 3. The point (2, 3) is the intersection of the straight lines represented by the two equations. See also Cramer's rule.A linear differential equation is of first degree with respect to the dependent variable (or variables) and its (or their) derivatives. As a simple example, note dy/dx + Py = Q, in which P and Q can be constants or may be functions of the independent variable, x, but do not involve the dependent variable, y. In the special case that P is a constant and Q = 0, this represents the very important equation for exponential growth or decay (such as radioactive decay) whose solution is y = ke^{−Px}, where e is the base of the natural logarithm.* * *
Universalium. 2010.
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Linear equation — Linear Lin e*ar (l[i^]n [ e]*[ e]r), a. [L. linearis, linearius, fr. linea line: cf. F. lin[ e]aire. See 3d {Line}.] 1. Of or pertaining to a line; consisting of lines; in a straight direction; lineal. [1913 Webster] 2. (Bot.) Like a line;… … The Collaborative International Dictionary of English
linear equation — n. an algebraic equation whose variable quantity or quantities are in the first power only and whose graph is a straight line (Ex.: 2x + 3y 5 = 0) … English World dictionary
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.Linear equations can have one, two, three or more variables. Linear equations occur with… … Wikipedia
linear equation — tiesinė lygtis statusas T sritis fizika atitikmenys: angl. linear equation vok. lineare Gleichung, f rus. линейное уравнение, n pranc. équation linéaire, f … Fizikos terminų žodynas
linear equation — noun a polynomial equation of the first degree • Hypernyms: ↑equation … Useful english dictionary
linear equation — noun Date: 1816 an equation of the first degree in any number of variables … New Collegiate Dictionary
linear equation — noun A polynomial equation of the first degree (such as x = 2y 7) … Wiktionary
linear equation — noun an equation between two variables that gives a straight line when plotted on a graph … English new terms dictionary
linear equation — lin′ear equa′tion n. math. a first order equation involving two variables: its graph is a straight line in the Cartesian coordinate system … From formal English to slang
linear equation — /lɪniər əˈkweɪʒən/ (say lineeuhr uh kwayzhuhn) noun an equation, all of whose variables are in the first degree … Australian English dictionary