Team. Won. Drawn. Lost. Points
...A ...... 2 ........ 2 ......... 0....... 26
...B ...... 1 ........ 3 ......... 1 ........ 18
...C ...... 0 ........ 3 ......... 3 ....... 18
...D ...... 1 ........ 2 ......... 1 ....... 19
...E ...... 2 ........ 1 ........ 0 ........ 21
Q) Given that each team plays the others TWICE, if all the remaining matches are draws, what fractions of the teams will have Less than 30 points?
So far I ve figured out that the points earned from a draw is 5, and that there are 9 matches left to play (since 20 is the total and 11 are already played from the table). I also worked out that the maximum overall points from the 20 matches (for all the teams) put together is 192. I m not sure if that was of any use though.
But I still can't seem to understand how to get the final scores for all the teams. Can anyone help me with that.
Thanks in advance :)
PS. I know this looks like a really easy question but I'm really having a hard time grasping it, so your help is more than appreciated
Edit: Here is the link to the question, it shows the table more clearly and has the complete set of questions
You have to solve the following system of equations: $$\begin{cases}2x+2y&=26\\x+3y+z&=18\\3y+3z&=18 \\ x+2y+z&=19 \\ 2x+y&=21\end{cases}$$
By evaluating this you can notice, that this system is contradictory (equations for A and E suggest, that $y=5$, but for B and D shows, that $y=-1$)