Absolute values

imo b

IMO B
lxl=lyl?
1) x-y=6
x=3 y=-3 yes condition satifies 1 and the answer is yes but
if x=9 y=3 No hence insuffient
2)x+y=0
x=-y
so Yes Suffienct

I think it diff way and i just want to know whether my way is correct or not. I think for proving mod x = mod y
we need to prove, if we take out mode... x = y ( if both are > 0) and -x = -y ( if <0)
coz by def of mode , mod x = x if x >0
mod x = -x if x<0
So, do we need to prove both condition in the ques below..or not.

Going by my method.
1.x-y =6
....>>> Not Suff
2. x+y=0, x=-y
utting back...mod(-y) = mod(y ) ....

... y = y ( If Y >00
-y = y( if y<0 )...not true. ....so B Insuff


taking together

x-y=6
x+y=0

x =3,y =-3
Here again comes my ques.
Do we have to put values and consider mode by >0 and <0


Pls f any1 can explain

but i just wanted to know..do we need to prove both the equations.