A linear equation is an equation that has the form

`{\ \ a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=b} `

`a_1,a_2`, etc. are called the coefficients of the equations and `b` is called the constant term. Variables in linear algebra are usually denoted by `x_n` instead of `x, y, z,` etc. because real world problems can have millions of variables. Problems in this text will have no more than `5` or `6.`
Terms that appear on the left side of a linear equation must have a power of exactly `1.` Terms that appear on the right hand side must have a power of zero.

Examples

`1. \ \ 2x_{1}-5x_{2}+x_{3}=9`
a linear equation

`2. \ \ x_{1}+2x_{2}+2\ \sqrt {x_{3}}=1\ `
NOT a linear equation because of the square root. A square root `\ \ \sqrt {x_{3}} ` is the same as ` x_{3}` to the power ` 1/2` and not to the power ` 1.`

`3. \ \ -10x_{1}+2x_{2}=0`
a linear equation

`4. \ \ x_{1}x_{2}+2x_{3}=0`
NOT a linear equation because `\ \ x_{1}x_{2}` is a term of power `2.`