User:Ascii/Definition:Linear Equation

Definition
A linear equation is a polynomial equation of the form:
 * $a x + b = 0$

such that $a \ne 0$.

General Definition
= Notes = * Presenting a linear equation as of the form ax = b as an alternative. == Example == === Example 1 === 3x = 15 This is solvable over N. === Example 2 === 7x + 49 = 0 This is solvable over Z. It is not solvable over N, however, and this may be mentioned as a motivation for Z or negative numbers. Possible mention of Diophantine equations here. === Example 3 === 3x + 11 = 0 This is solvable over Q Similar things could be said about it being a motivation for extending Z. === Example 4 === 3x + 4y = 18 A lot of commentary could be made here: Finite solutions over N. Infinite solutions over Z with a mention of linear combinations and ways to generate them. Similar for Q.

Also see

 * Solution to Linear Equation


 * Definition:Quadratic Equation
 * Definition:Cubic Equation
 * Definition:Quartic Equation
 * Definition:Quintic Equation