How do you solve the simultaneous equations x^2+y=1 and -x+y=-1

First rearrange the second equation so that it's equal to y. You do this by adding x and y to both sides of the equation. You should then have y=x-1. Next you should sub y=x-1 into the first equation, x²+y=1. You should now be left with x²+x-1=1. This can be rearranged by subtracting 1 from each side to create the quadratic equation x²+x-2=0. This can be solved in which ever way you prefer; I would factorise it, leaving you with (x+2)(x-1)=0. Therefore x=-2 or x=1