I have got a set $ F=\{{0,1,2}\}$ and I know that $(F,+,*)$ is a field.
Now I have to solve the two equations: $$ 2x+2y= 1$$ $$1x+2y=2$$
By calculating the answer according to the field tables I get $x=-1, y=0$ which is obviously wrong. I can't seem to find where I made the mistakes. Anyone got a right answer? Thanks!
Your answer is correct. You simply have to remember that '-1' in this field is whatever number, when added to 1, yields 0. That is, '-1' is another name for 2. [think: 'modular arithmetic']