I am trying to find the adjacent bfs for the following tableau. So far I understand that it has an alternative solution because there is $x_4$ a nonbasic decision variable that has a 0 coefficient in the row of z. Thus I choose my pivot column as the column of $x_4$ but all the entries of that column are negative and I cannot implement ratio test. I am stuck. Is there a way to solve this? I thought about Bland's rule but I suppose it only works when there is a tie in the ratio test (so I have to be able to implement ratio test in the first place.) I would be grateful if you can show me a way to start simplex.
$$ \begin{array}{ |c||c|c|c|c|c|c|c|c||c|} \hline &z&x_1&x_2&x_3&x_4&x_5&x_6&x_7&\rm RHS\\ \hline \hline &1 &12 &5 &3 &0 &0 &0 &0 &120\\ \hline \hline x_5& 0 &7 &4 &-3 &-4 &1 &0 &0 &8\\ x_6 &0 &-1 &1 &2 &-3 &0 &1 &0 &4\\ x_7&0 &4 &-3 &0 &-1 &0 &0 &1 &3\\ \hline \end{array} $$