Solve the following system of equations

$-25x-6y-z=-67$

$-15x-10y-2z=-33$

$20x+6y+z=52$

using the Gauss$-$Jordan method.

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ This system has exactly one solution. The solution is

$($Type an exact answer in simplified form.$)$

B$.$ This system has infinitely many solutions of the form $$

$,$z$),$ where $z$ is any real number.

$($Type expressions using $z$ as the variable.$)$

C$.$ This system has no solution.