Question

Provide the complete solution for the following linear congruences.

3x-2 = 7 (mod 11)
5 = 4x-1 (mod 9)

(I didn't understand the previous solution I got) Provide the complete solution for the following linear congruences.

3x-2 = 7 (mod 11)
5 = 4x-1 (mod 9)

(I didn't understand the previous solution I got) @Mathematics

Answer 1

I get to the point where I have -6 =11y (mod9) but I'm not sure what to do then

Answer 2

and remember that these are linear congruences (just didn't know how to make the equal sign with 3 lines)

Answer 3

I don't think you can divide both sides by 3 in linear congrueces

Answer 4

the way I was doing it was by converting it to a linear diophantine equation then using the extended euclidian algorithm to solve it

Answer 5

but I don't know what to do when the variable is one the inside of the linear congruence

Answer 6

My best guess is that it doesn't matter what side the variable is on since it's a congruence. I'm not positive, but that seems right to me.

Answer 7

how do I find y for -6 =11y (mod9)

Answer 8

Once again, I'm not entirely positive this is the right way to go, but -6 = 5 (mod 9), so it seems like that equation is the same as 11y = 5 (mod 9).

Answer 9

my bad, -6 = 3 (mod 9), so 11y = 3 (mod 9)