# Fundamental Mathematics/Arithmetic/Linear equation

A linear equation is an equation that may be put in the form

${\displaystyle a_{1}x_{1}+...+a_{n}x_{n}+b=0}$

## One variable

With just one variable, the equation can be put in the form

${\displaystyle ax+b=0}$

with the solution

${\displaystyle x=-{\frac {b}{a}}}$

where ${\displaystyle a\neq 0}$

## Two variables

If there are two variables, a linear equation may be put in the form

${\displaystyle ax+by+c=0}$

where the variables are ${\displaystyle x}$ and ${\displaystyle y}$, and the coefficients are ${\displaystyle a}$, ${\displaystyle b}$ and ${\displaystyle c}$.