# Definition:Linear Equation

## 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 $1$.

## Example

The equation $b = a_1 x_1^2 + a_2 x_2^2 + a_3 x_3^2$ is *not* linear because all the $x$ terms are squared.

## Sources

- 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $4$: Lure of the Unknown