Brute forcing simultaneous equations involving Complex Numbers

So I have many students coming up to me and saying, “Mr Teng, How do you know which to substitute away or when to introduce when doing simultaneous equations for complex numbers?”
Here is a lesser method that will give you the answers. It is definitely a clearer method that involves less pitfalls. This method is self-explanatory so I’ll let the working do the talking. Say we want to solve the following

Let (clearly, ) , and

From (1), we have

, and

From (2), we have

, and

Solving (3), (4), (5), (6), we find

Thus, and