Definition:Linear Equation

Definition
A linear equation is an equation in the form:


 * $y = a_1 x_1 + a_2 x_2 + \cdots + a_n x_n$

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

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

Example
The equation $y = ax_1^2 + bx_2^2 + cx_3^2$ is not linear because all the $x$ terms are squared.