I'm taking an abstract algebra class. I have a question in which I am given two systems of linear congruences.

I'm taking an abstract algebra class.  I have a question in which I am given two systems of linear congruences.  I am given the solution to each system and asked to confirm the solutions using the Chinese Remainder Theorem.  However, in both cases, my systems contain non-prime mod values...so, I'm not sure how I am supposed to use the Chinese Remainder Theorem to confirm the solutions.  One of the systems is: x = 1 mod 8 and x = 5 mod 10.  The solution given is x = 25 mod 40.  How do I confirm the answers using the Chinese Remainder Theorem?  I see that GCD(8, 10) = 2...and that 2 divides (5-1 =4).  I'm just not sure how to proceed, since all the examples in my text involved the Chinese Remainder Theorem.  Thoughts?

:−ℎ ℎ ℎ ≡1 8 ≡5 10 8 = 2.2.2 ℎ 10 = 2.5 => ≡5 5 (8,10) = 2 ∶− ℎ≡5=>ℎ 2 ≡1 2 ≡0 5 ℎ≡1 8, ≡1 2 ≡0 5 ℎ≡1 8 ℎ ≡0 5 (8,5) = 1 ℎ ℎ=1 , = 8,...