a$)$ Solve the linear system $3x-y-11=0$ and $x+2y+1=0.$

b$)$ Show that the line with the equation $9x+4y-19=0$ passes through the point where the lines in part a$)$ intersect.

c$)$ Determine the values of $c$ and $d$ if $9x+4y-19=0$ is written in the form $c(3x-y-11)+d(x+2y+1)=0.$