# Solutions of the systems of congruences

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Find all solutions of each of the systems of congruences:-

(a) x is congruent to 1 (mod 2) (d) 4x is congruent to 2 (mod 6)

x is congruent to 2 (mod 3) 3x is congruent to 5 (mod 7)

x is congruent to 3 (mod 5) 2x is congruent to 4 (mod 11)

(b) x is congruent to 1 ( mod 3) (e) x is congruent to 1 (mod 3)

x is congruent to 3 ( mod 5 ) x is congruent to 2 (mod 4)

x is congruent to 5 ( mod 7) x is congruent to 3 ( mod 7)

x is congruent to 4 (mod 11)

(c) 3x is congruent to 1(mod 5) (f ) 2x is congruent to 1 (mod 5)

4x is congruent to 6 (mod 14) 3x is congruent to 9 (mod 6)

5x is congruent to 11 ( mod 3) 4x is congruent to 1 (mod 7)

5x is congruent to 9 (mod 11

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##### Solution Summary

This solution is comprised of a detailed explanation for finding all solutions of each of the systems of congruences.

It contains step-by-step explanation for finding all solutions of each of the systems of congruences of the following :

(a) x is congruent to 1 (mod 2), x is congruent to 2 (mod 3), x is congruent to 3 (mod 5),

(b) x is congruent to 1 ( mod 3), x is congruent to 3 ( mod 5 ), x is congruent to 5 ( mod 7),

(c) 3x is congruent to 1(mod 5), 4x is congruent to 6 (mod 14), 5x is congruent to 11 ( mod 3),

(d) 4x is congruent to 2 (mod 6), 3x is congruent to 5 (mod 7), 2x is congruent to 4 (mod 11),

(e) x is congruent to 1 (mod 3), x is congruent to 2 (mod 4), x is congruent to 3 ( mod 7), x is congruent to 4 (mod 11),

(f) 2x is congruent to 1 (mod 5), 3x is congruent to 9 (mod 6), 4x is congruent to 1 (mod 7), 5x is congruent to 9 (mod 11)

Solution contains detailed step-by-step explanation.

###### Education

- BSc, Manipur University
- MSc, Kanpur University

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