What -4x -4y = 0 and -5x -3y = -6?

Divide  the first  equation through by   -4  and we get that

x + y  = 0   which implies  that   y  = -x

Sub this into  the second equation  for  y   and we have that

-5x  - 3 (-x)  = -6

-5x  + 3x =  -6

-2x  = -6   divide both sides  by  -2

x  = 3  

And  

y =  -x  =  -3