Can you explain the procedure used to find the rate law?

Basically, you compare two initial concentrations of the reactants. Initially you start off with the variables x and y. To find x, you take a set of concentrations where the base of y's that are being compared are the same. That way, everything cancels out just leaving the x to solve. Then the same process can be done to solve y. Then there you have it. RATE LAW!