User:Ascii/Definition:Linear Equation/General Definition

Definition

A linear equation is an equation in the form:

$b = a_1 x_1 + a_2 x_2 + \cdots + a_n x_n$

where all of $a_1, \ldots, a_n, x_1, \ldots x_n, b$ are elements of a given field.

The point is that all the indices of the $x$ and $y$ terms in such an equation are $1$.