Solutions of this set of linear congruences using Chinese Remainder Theorem?

Question

Suppose m1, m2, ..., mk are positive integers > 1, not necessarily pairwise relatively prime. Also Suppose a1, a2, ..., ak ∈ Z. What can be said about the solutions of the following set of linear congruence equations? x ≡ a1 (mod m1), x ≡ a2 (mod m2), x ≡ a3 (mod m3), ..., x ≡ ak (mod mk).