Finding critical points of a non-linear sysytem

[dp182]

Homework Statement

I am trying to find the critical points of the system x¹=x²+y²-2xy-1 and y¹=y+x-2

Homework Equations

x¹=x²+y²-2xy-1=0
y¹=y+x-2=0

The Attempt at a Solution

I tried to solve for zero but I end up with multiple solutions way more then I should need any help answering would be helpful

 

[hunt_mat]

So what I did was write y=2-x and substituted into x^2+y^2-2xy-1=0 to get an equation for x, I solved this and find x and then I used the answers to find y. the two critical points are (0.5,1.5) and (1.5,0.5)

 

[dp182]

thanks so much that really helps alot