Substitution method is one of the ways to solve this system.
-5x+y=4 and 4x-4y=16.
First we will divide the second equation with number 4 and get
x-y=4 => x=y+4 than we will replace x in the first equation
-5(y+4)+y=4 => -5y-20+y=4 => -4y=4+20 => -4y=24 => y=-6
x-(-6))=4 => x+6=4 => x=4-6=-2 (x,y)=(-2,-6)
Good luck!!!