With this kind of question it really helps to break it down into bite-sized chunks to make it easier to write out. If you look at this carefully, you really have to do the difficult task once, and the rest will follow by analogy. For example, when you are subtracting equation 2 from equation 1, you have to calculate . In general, this is what we get from a term like that

You can substitute anything for and anything for . For example, this immediately gives the LHS of the first linear equation

The RHS for this equation can be obtained by using . We have the RHS

Here is what happens when you subtract the 2nd, 3rd and 4th equations from the 1st respectively. The LHSs are

The RHSs are

Granted, these are quite a bit more unappetizing in terms of their content, but their form is superb because they are all linear. And with linear equations it is relatively you can use linear algebra to solve them.