A **linear equation** in $m$ variables (where $m$ is some [[wp>natural number]]) is an equation of the form 
\[ a_1x_1+a_2x_2+\dots+a_mx_m=b\]
where $a_1,a_2,\dots,a_m$ and $b$ are fixed numbers (called **coefficients**) and $x_1,x_2,\dots,x_m$ are [[variables]].