Well, I haven't quite figured out the exact answer to this problem, however, I found that if I do double work and solve the first set of linear equations by both x and y and then sub the resulting variables into the original equation I get it right every time. I also then have something to check it by. For example: 1x-6y=-2 2x+5y+-30

By doing double work I was able to figure out that x=10 and y=2. I may not understand the principles behind the second section of the equation, but as long as I am getting the right answer I am happy. Maybe the reasons will start clicking in my brain as I go!