Question

Can somebody explains what I did wrong? Find the points (0,0) and (-1,-1). Eq1) x^2=-y, Eq2) x=-y^2
I replace Eq1 in Eq2--> x=(x^2)^2-->x=x^4--> x^4 -x=0-->x(x^3 -1)=0--> x(x+1)(x^2 +x-1)=0
I got x=0, and x=-1. I plug those into the Eq1 I get 0^2=-y and -1^2=-y. I got the points (0,0) and (-1,-1) but I feel I did something wrong. I got the points but what about the (x^2 +x-1). Why is it still around? What should I do with it? Should there be another point?

Answer 1

I did it this way:
x^2 = -y and x = -y^2
sub the 2nd into the first:
(-y^2)^2 = -y
y^4 + y = 0
y(y^3 + 1) = 0
then y = 0 or y^3 = -1 ---> y = -1

in the 2nd,
if y = 0, then x = 0
if y = -1, then x = -(-1)^2 = -1

so there are your (0,0) and (-1,-1)

following yours ......
the 1st into the 2nd
the 1st: x^2 = -y or y = -x^2

2nd: x = -y^2
x = -(-x^2)^2 = -x^4
x^4 + x = 0
x(x^3 + 1) = 0
same pattern as mine when I solved for y

can you see your error? Watch those nasty negatives when you square them

-y^2 means -(y^2)

Answer 2

I got it. Thank You