The equation is x-|x|=y-|y| and I need to make a graph for it.

So I thought I should solve it by breaking it down to 4 different equations, which would be -

x - x = y - y => 0=0

x - x = y + y => 0=2y => y = 0

x + x = y - y => 2x=0 => x = 0

x + x = y + y => 2x=2y => x = y

But this isn't correct, riight? I don't know what else to do, kinda lost here.

Would love some help, thanks.