A linear equation in $m$ variables (where $m$ is some 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.