how do you solve a modular system of equations like x= 2 mod 7 and x= 3 mod 3 or something like that?

Answer 1

You should now that the necessary and sufficient condition for a=b(mod n) is
a-b= multiple of n
so x=2(mod7) can be written as
x-2=k*7 so x= 2+k*7 with k an integer
In the same way
x=h*3