Solving Linear Congruence ax ≡ b (mod N)

Positive integers $x,y,z \le 100$ satisfy \begin{align*} 1099x+901y+1110z &= 59800 \ 109x+991y+101z &= 44556 \end{align*} Compute $10000x+100y+z$.

Source: 2012-2013 Winter Online Math Open