Question

Find the value of y in the mod 11 system. 10 + y = 1

Answer 1

y=2

Answer 2

In the mod 11 system you have {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} From there on you don't write 11 since 11 is congruent to 0 mod 11, and 12 is congruent to 1 mod 11 and so on. Thus you can rewrite your equation as 10+y congruent to 12 (adding 11 to your right hand side since adding by 11 to any number in the mod 11 system is valid-think about when you add 0 to any number when you are in the real number system). Thus your answer is y=2.