linear equation

$a_1x_1+\cdots+a_nx_n=b$ — every variable alone, never multiplied or raised to a power.

A linear equation in variables $x_1,\dots,x_n$ has the form $a_1x_1+a_2x_2+\cdots+a_nx_n=b$ , fixed real coefficients and constant. Every variable appears alone, multiplied only by a constant, added to the rest — never multiplied by another variable, raised to a power other than $1$ , or fed into a function like $\sin$ or $\sqrt{\ }$ . An equation breaking these rules is nonlinear.