(Solved): solve the system 3x is congruent to 2 mod 4 4x is congruent to 1 mod 5 6x is congruent to 3 mod 9 ...

Expert Answer

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Given, the first congruence:     

To find the modular inverse of 3 modulo 2^2, it is observed that   . Therefore, the modular inverse of 3 is 3 itself.

Multiplying both sides by 3, we get:  
Second congruence:     

To find the modular inverse of 4 modulo 5, we can observe that   . Therefore, the modular inverse of 4 is 4 itself.

Multiplying both sides by 4, we get:   

Third congruence:  
  

To find the modular inverse of 2 modulo 3,It is observed that   . Therefore, the modular inverse of 2 is 2 itself.

Multiplying both sides by 2, we get: