Point counting $K_0(Var/\mathbb{F}_q) \to \mathbb{Z}$ induced by $[X] \to \#X(\mathbb{F}_{q^e})$ is a ring homomorphism, so $$[X] + [Y] = 0$$ would imply $\#X(\mathbb{F}_{q^e}) +\#Y(\mathbb{F}_{q^e}) = 0$. And this can only happen if $X$ and $Y$ are the empty varieties.
Artur Jackson
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