Cramer's Rule for 3 x 3's works, pretty much, the same way it does for 2 x 2's -- it's the same pattern.
Let's solve this one:
First, find the determinant of the coefficient matrix:
(I'm just going to
crunch the determinants without
showing the work -- you should check them!)
|For a 3 x 3, we have 3 more determinants to find:||,||, and|
|... Then we'll have|