How to apply cramer's rule in this system

Question

The system consists of the following equations:

1/x - 2/z = -3

2/y + 3/z = 5

1/x - 1/y = -2

Solve for Z using the cramer's rule

Answer 1

As far as I know Cramer's rule only applies to linear systems, which this certainly is not.

However, if you let a=1/x, b=1/y and c=1/z, you will convert it to a system to which Cramer's rule does apply. Then you can solve for a, b and c by Cramer's rule and then go back to the inverses.

If you don't remember Cramer's rule, it tells you how to use determinants to solve linear systems.