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Answer:
The smallest positive integer solution to the given system of congruences is 30.
Step-by-step explanation:
The given system of congruences is
where, m and n are positive integers.
It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as
Now, we can say that m>n because m and n are positive integers.
For n=1,
19 is not divisible by 5 so m is not an integer for n=1.
For n=2,
The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is
Therefore the smallest positive integer solution to the given system of congruences is 30.