In a soccer match,each team had to play with every other team once. If there were 6 teams,how many matches would be played

Each of the 6 teams plays 5 others so at first sight it looks as though there are 6*5 = 30 matches.  However, this counts each match twice, so, in fact, there are 30/2 or 15 matches in total.  

To  expand upon Alan's answer, consider this:

Team "6" plays the 5 other teams

Team "5" plays the 4 other teams (We've already counted their game against team "6")

Team "4" plays the 3 other teams (We've already counted their games against teams "6" and "5")

etc.

So the total games played = 5 + 4 + 3 + 2 + 1 = 15

Which just happens to be the sum of the first 5 positive integers. There's a "formula" for this which is just :

(n)*(n-1) / 2 where n = the number of teams involved.

So we have (6)*(5) / 2 = 30 / 2 =15 ......which is exactly what Alan found...