Editing System of linear equations (section)

===Geometric interpretation===
For a system involving two variables (''x'' and ''y''), each linear equation determines a [[line (mathematics)|line]] on the ''xy''-[[Cartesian coordinate system|plane]]. Because a solution to a linear system must satisfy all of the equations, the solution set is the [[intersection (set theory)|intersection]] of these lines, and is hence either a line, a single point, or the [[empty set]].

For three variables, each linear equation determines a [[plane (mathematics)|plane]] in [[three-dimensional space]], and the solution set is the intersection of these planes. Thus the solution set may be a plane, a line, a single point, or the empty set. For example, as three parallel planes do not have a common point, the solution set of their equations is empty; the solution set of the equations of three planes intersecting at a point is single point; if three planes pass through two points, their equations have at least two common solutions; in fact the solution set is infinite and consists in all the line passing through these points.{{sfnp|Cullen|1990|p=3}}

For ''n'' variables, each linear equation determines a [[hyperplane]] in [[n-dimensional space|''n''-dimensional space]]. The solution set is the intersection of these hyperplanes, and is a [[flat (geometry)|flat]], which may have any dimension lower than ''n''.