# Family Of Linear Equations

Algebra Level 5

Let $$\{a_i\}$$, $$\{b_i\}$$ for $$i=1\to 2014$$ be two sequences such that the unique x-intercept of $$y=a_ix+ib_i$$ is $$b_i$$ and the unique y-intercept is $$a_i$$. Determine the value of $\left(\displaystyle\sum_{i=1}^{2014}a_i+b_i\right)\pmod{1000}$

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