Consider the following system of linear congruences.

$x-=4,(mod5)$

$x-=11,(mod36)$

$($a$)$ Find all values of the variable $x$ which satisfy the system and show your work.

$($b$)$ Suppose we add the following congruence: $x-=29(mod54)$ to the system above. What values of $x$ satisfy the new system? Show your work.