Solve this 4x4 matrix using Cramer's rule

(1-a1-a2 ; a1 ; a2 ; 0)

(b1 ; 1-b1-a2+c2 ; 0 ; a2-c2)

(b2 ; 0 ; 1-b2-a1+c2 ; a1-c1)

(0 ; b2+c2 ; b1+c1 ; 1-b1-c1-b2-c2)

all 4 rows equal zero and the variables to be found (going across the rows) are w, x, y and z.

When I tried to solve the first determinant I got 4 brackets with 3, 4, 4 and 5 elements in and the multiplying out got too confusing so I am not sure if it was right or not.

My teacher said Cramer's rule is the easiest way to solve so I want to do it by this method but I've never been taught it and I can't find an example using algebra.