first because 5x+5y=0 you can factor the 5 from equation so:
5(x+y)=5(0) => x+y=0
and by solving for x using elimination method
-8x+y=36
x+y=0
by subtracting both x and y we get
-9x=36 => x=-4
by inputing x into the "x+y=0" equation we get:
-4+y=0 => y=4