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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, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
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 ...
Consistent and inconsistent equations. Whether or not there exists a set of values to satisfy a given system of equations. In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that ...
Successive over-relaxation. In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process.
Equating coefficients. In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
is a horizontal line with y-intercept a0. The graph of a degree 1 polynomial (or linear function) f(x) = a0 + a1x, where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1. The graph of a degree 2 polynomial. f(x) = a0 + a1x + a2x2, where a2 ≠ 0. is a parabola. The graph of a degree 3 polynomial.
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Linear inequality. In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality: [1] < less than. > greater than. ≤ less than or equal to. ≥ greater than or equal to. ≠ not equal to.