Question 449034

A system of linear equations means two or more linear equations. (In plain speak: 'two or more lines') If these two linear equations intersect, that point of intersection is called the solution to the system of linear equations.

Systems of equations that have three variables are systems of planes. Since all three variables equations such as {{{2x + 3y + 4z = 6}}} describe a a three dimensional plane. 

Like systems of linear equations, the solution of a system of planes can be {{{no }}}{{{solution}}}, {{{one }}}{{{solution}}} or {{{infinite }}}{{{solutions}}}.

If there is {{{no}}}{{{ single }}}{{{point}}} at which {{{all}}}{{{ three }}}{{{planes}}}{{{ meet}}}, the system of 3 variable equations has {{{no}}}{{{ solution}}}. 

If the three planes {{{intersect}}}, then the three variable system has {{{1}}} point in common, and has  {{{one }}} solution.

If the three planes intersect and the three variable system has a {{{line}}} of intersection,it will have an {{{infinite }}} number of {{{solutions}}}.