Linear Equation

Definition

Let

• $x_1,\dots ,x_n$ : Variables of size $n$
• $b$ : Constant
• $a_1,\dots ,a_n$ : Nonzero constants

Linear equation is defined as $a_1{x}_1+\cdots +a_n{x}_n=b$

Remark

We often say the $a_1,\dots ,a_n$ constants as coefficients instead.

A linear equation does not involve any products or roots of the $x_i$ variables, e.g., $x+3y=7$, $\frac{1}{2}x-y+3z=-1$, and not $x+3y^2=4$, $2x+2y-xy=5$.