Critical point classification II

Find and classify the critical points of

This is what I got for this function f(x,y) = x^2 - 4xy + y^2 - x - y.
df/dx = 2x-4y-1
df/dy=2y-4x-1 =>4y-8x-2
=>-6x-3=0
So I added them together but I multiplied df/dy by 2
-6x=3 add 3 on both sides
x=-1/2 divide by -6
Then I solved for y
2y-4(-1/2)-1
2y+2-1=0
2y=-1
y=-1/2
My critical point is (-1/2,-1/2)
dxx=2
dxy=-4
dyy=2
So you end up with 2*2-4^2 which would be 4-16 then I got -12 so that means its a saddle.