We examine the general weighted Lane-Emden system
$-Δ u = ρ(x)v^p, -Δ v= ρ(x)u^θ, u,v>0 \;\mbox{in }\;\mathbb{R}^N$
where $1 <p≤qθ$ and $ρ: \mathbb{R}^N \to \mathbb{R}$ is a radial continuous function satisfying $ρ(x)≥q A(1+|x|^2)^{\frac{α}{2}}$ in $\mathbb{R}^N$ for some $α≥q 0$ and $A>0$. We prove some Liouville type results for stable solution and improve the previous works [
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