Linear Equation

A linear equation is an equation that can be put in the form a sub 1 times x sub 1 plus other such terms plus b equals zero, where the x terms are the variables and b and the a terms are coefficients, often real numbers, that are not all zero. The solutions of a linear equation are the values that make the equality true when substituted for the unknowns; with one variable there is exactly one solution provided its coefficient is nonzero, and with two variables each solution can be read as the Cartesian coordinates of a point, so the full solution set forms a line in the plane, which is the origin of the term linear for this type of equation. More generally, the solutions of a linear equation in n variables form a hyperplane, a subspace of dimension n minus one, in n-dimensional Euclidean space, and linear equations occur constantly throughout mathematics and its applications in physics and engineering, partly because nonlinear systems are so often well approximated by linear ones. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/