Markov chain Probabilities

A Markov chain on state space {1,2,3,4,5} has transition matrix

$\begin{pmatrix} 0 & 0 & 1 & 0 & 0 \\
0 & 0 & 4/{5} & 1/{5} & 0 \\
0 & 1/{6} & 2/{3} & 0 & 1/{6} \\
0 & 0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0 & 1 \\
\end{pmatrix}$

The process starts in state 1.
d) Calculate the expectation of the number of visits to state 2 before absorption.
Solution: $v_1=v_3$
$v_2=1+(4/5)v_3$
$v_3=(1/6)v_2+(2/3)v_3$
I am not sure how to get the above three equation? can you help please?
These are easily solved to give $E(V)=v_1=5/6$