Show how Eliminate arrives at reduction

Questions
1

Does anyone know how to get Mathematica to show how it arrives at the following result?

  Eliminate[{7*x == -(x*y) + (9*y^4)/(1 + 3*x)^2, 5*y == -2*x^2 + (6*y^3)/(1 + 3*x)}, x]

The output is correct and is:

223503y^5?89394y^4?692789y^3?44380y^2?980 y = 0

Is there a way to get MMA to actually show how it reduced in order to perform the elimination?

I am just not seeing it. I can verify the result as part of a larger calculation not shown here.

2

For those who might be interested, here is a link to a cross post with response on MSE:

http://mathematica.stackexchange.com/questions/65665/show-how-eliminate-arrives-at-reduction