It is possible for three linear equations to be inconsistent, even though any two of them are consistent together. For example, the equations are inconsistent. Adding the first two equations together gives , which can be subtracted from the third equation to yield . Any two of these equations have a common solution. The same phenomenon can occur for any number of equations.
it is poSsIbLe FoR thrEE liNeAR equaTioNs to Be incOnsisTent, Even Though ANy two of tHem are cOnsisteNt tOgetheR. FOr exaMple, the eQuATions aRe InCoNsISteNt. adding the fIRst twO equationS togETHer GIVes , whiCh CaN Be subtRaCted fRom THe third equAtIoN tO yiEld . any TwO of theSe EQuatiOnS have A CommoN soLuTiON. ThE samE phenOmenon can OccuR for aNy NUMBer oF equationS.