System of Congruences, math homework help

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Mathematics

Description

Explain why a solution does not exist for the following systems of congruences. Your work should include reduction to a single equation and the greatest common divisor.

(1) z ≡ 1 (mod 8)

z ≡ 4 (mod 10)

(2) w ≡ 3 (mod 10)

w ≡ 9 (mod 15)

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