HMMT November 2021 U19

Integers $0 \leq a, b, c, d \leq 9$ satisfy

$\begin{gathered} 6 a+9 b+3 c+d=88 \\ a-b+c-d=-6 \\ a-9 b+3 c-d=-46 \end{gathered}$

Find $1000 a+100 b+10 c+d$ .

Dataset text NuminaMath olympiads. Quoted with source.

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