equation solving – Stationary Distribution of Markov Chain

I’m trying to compute the stationary distribution of the following Markov chain:

$$P=left(
begin{array}{cc}
p_{11} & p_{12} \
p_{21} & p_{22} \
end{array}
right)$$

I know you have to solve the equation:

$$pi = pi P$$

So, going through the standard approach…

pi = ( {
   {Subscript(pi, 1), Subscript(pi, 2)}
  } )
pi.P // FullSimplify

Out = {{p11 Subscript(pi, 1) + p21 Subscript(pi, 2), 
  p12 Subscript(pi, 1) + p22 Subscript(pi, 2)}}

And then solve the linear equations using the “Solve” command:

Solve({p11 Subscript(pi, 1) + p21 Subscript(pi, 2) - Subscript(pi, 
     1) == 0,
           
   p12 Subscript(pi, 1) + p22 Subscript(pi, 2) - Subscript(pi, 2) == 0,
           Subscript(pi, 1) + Subscript(pi, 2) == 1}, {Subscript(pi, 
   1), Subscript(pi, 2)}) // FullSimplify

The thing is that I get no solution.

Why does this happen?