Linear Equations
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Problem Description
A linear equation is an equation that is written for two different variables. This equation will be a linear combination of these two variables, and a constant can be present. Surprisingly, when any linear equation is plotted on a graph, it will necessarily produce a straight line  hence the name: Linear equations.
A linear equation can be written in different ways. Any simple equation in x and y can be termed as a linear equation if it follows a certain set of rules. For example, the highest (and the only) degree of both  x and y  variables in the equation should be 1. Other than that, constants (zero degree variables) can be there.
Bounds Chart
Step Chart
Improvement Table
Complexity Classes  Algorithm Paper Links  Lower Bounds Paper Links 

Exp/Factorial  
Polynomial > 3  
Cubic  [GaussianJordan Elimination (150)]
[Cholesky (1940)] 

Quadratic  Conjugate Gradient (1952)  
nlogn  
Linear  
logn  Harrow (Quantum) (2009) 