Solve System of Congruences Using CRT

[needmathshelp]

Hi, i know how to do the CRT but I'm kind at a loss with this one. Can anyone help me please?

Explain why the Chinese Remainder Theorem does not apply directly to the following
system.
x = 5 mod 6
x = 17 mod 21

Determine an equivalent system of equations to which the CRT applies and hence solve this
system of congruences.

Cheers.

 

[vela]

What does the Chinese remainder theorem state? In particular, what conditions must be satisfied before it can be applied? Which condition or conditions aren't satisfied by this example?