Linear system of equations

The most simple type of linear system of equation is the intersection of two lines:

a x + b y = c
d x + e y = f

In three dimensions a similar problem is the intersection of three planes. Finding solutions to linear systems of equations falls under the field of linear algebra. Some methods of solving linear equations include: substitution and elimination of variables. A more sophisticated form of elimination is Gaussian elimination and Gauss-Jaurden elimination.