is there something i'm missing in my textbook? why the hell is y=1? and not -1?
Probably because the integer -1 is not an element of this field. Look again to the way they have defined it. This is consistent with the fact that the text shows there are only 2 solutions, and not infinite ones.
y+1=0 is correct
that means you have to look for the inverse element of 1 for the operation + in Z2
and that is the element 1
there is no such thing as substraction, only addition
you can also start from y+1=0, and add 1
y+0 = 1
Is this a troll post? The only real number solution here is y = -1
If you input the numbers from that 'solution', you get 2 for both equations which are obviously false. The actual solution is x = 1, y = -1, z = 0.