Solution (source code)

= Solution

A <stationary point> has zero <gradient>. The two <partial derivatives> give
$$
f_x=2x-1+y=0,\qquad f_y=x-3-2y=0.
$$
Solving this <system of linear equations> gives
$$
\boxed{(x,y)=(1,-1)},\qquad f(1,-1)=0.
$$