If a+b = 8, b+c = -3, and a+c = -5, what is the value of the product abc?

I've tried combining all of the equations together but I'm not sure if that's on the right track or not because after I get my answer it doesn't seem to make any sense.

a=3 b=5and c=-8 since we dd them all and get 0 so (a+b+c)*2=0 and 0/2=0 we do 0-8=-8 to get c,0-(-3)=3 to get a, and 0-(-5)=5 to get b.

so the product of abc=3*5*-8 and there is 1 negative number so the product is a negative number it is -(15*8)=(-120)

so a*b*c=-120