abstract:Solving%20system%20of%20linear%20equation%20(or%20linear%20systems%20or,%20also%20simultaneous%20equation)%20is%20a%20common%20situation%20in%20many%20scientific%20and%20technological%20problems.%20Many%20method%20either%20analytical%20or%20numerical,%20have%20been%20developed%20to%20solve%20them%20so,%20in%20this%20paper%20I%20will%20explain%20how%20to%20solve%20any%20arbitrary%20field%20using%20the%20different%20-%20different%20methods%20of%20system%20of%20linear%20equation%20for%20this%20we%20need%20to%20define%20some%20concepts.%20Like%20a%20general%20method%20most%20used%20in%20linear%20algebra%20is%20the%20Gauss%20Elimination%20or%20variation%20of%20this%20sometimes%20they%20are%20referred%20as%20%22direct%0Amethods%20%22Basically%20it%20is%20an%20algorithm%20that%20transforms%20the%20system%20into%20an%20equivalent%20one%20but%20with%20a%20triangular%20matrix,%20thus%20allowing%20a%20simpler%20resolution,%0AOther%20methods%20can%20be%20more%20effective%20in%20solving%20system%20of%20linear%20equation%20like%20Gauss%20Elimination%20or%20Row%20Reduction,%20Gauss%20Jordan%20and%20Crammer's%20rule%20etc.So,%20in%20this%20paper%20I%20will%20explain%20these%20method%20by%20taking%20an%20example%20also,%20in%20this%20paper%20I%20will%20explain%20the%20Researcher's%20works%20that%20how%20they%20explain%20different%20different%20methods%20by%20taking%20different%20example.%20And%20I%20worked%20on%20using%20these%20different%20methods%20in%20solving%20a%20single%20example,%20i.e.%20I%20will%20use%20these%20methods%20in%20an%20example.%0AIn%20this%20paper%20I%20will