Solve for $x$ and $y$
How should I find $x$ and $y$?
I thought of using the methods I learned in linear algebra but then I noticed that there is a square in the $x$ and $y$ variable so that makes these set of equations not linear. So, linear algebra doesn't apply here (please correct me if I am wrong).
A method I learned in high school is to divide the two equations together and to substitute it into the other. This is the way that my textbook shows too. But I don't know why this operation is valid i.e. does dividing the two equations really preserve the solution to the system? In linear algebra, as far as I know, dividing two equations together is not a valid row operation.
Therefore, I would like to know, what is the theory behind solving this kind of system of equations.