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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