Determine the value$($s$)$ of $h$ such that the matrix is the augmented matrix of a consistent linea system.

$\left[\begin{array}{ccc}6& 8& h\\ -3& -4& 1\end{array}\right]$

Select the correct choice below and, if necessary, fill in the answer box to complete your choic

A$.$ The matrix is the augmented matrix of a consistent linear system if $h($Use a comma to separate answers as needed. Type an integer or a simplified fraction.$)$

B$.$ The matrix is the augmented matrix of a consistent linear system if $h=($Use a comma to separate answers as needed. Type an integer or a simplified fraction.$)$

C$.$ The matrix is the augmented matrix of a consistent linear system for every value of $h.$

D$.$ The matrix is not the augmented matrix of a consistent linear system for any value of h$.$