1. Solve the following systems of congruences or explain why they do not have solutions. In...

   

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1. Solve the following systems of congruences or explain why they do not have solutions. In case there are solutions they must be given in the modulus that is the LCM of the congruence modulus. (a) (1 point) 13X=3 (mod 15), 2X = 6 (mod 10). (b) (2 points) X21 (mod 10), X2 3 (mod 187) = (c) (2 points) X+2Y 3 (mod 7), 3X+5Y=1 (mod 21). 1. Solve the following systems of congruences or explain why they do not have solutions. In case there are solutions they must be given in the modulus that is the LCM of the congruence modulus. (a) (1 point) 13X=3 (mod 15), 2X = 6 (mod 10). (b) (2 points) X21 (mod 10), X2 3 (mod 187) = (c) (2 points) X+2Y 3 (mod 7), 3X+5Y=1 (mod 21).