Question: Eliminating variables from a set of equations

First time posting here, hoping to find some help, and I may try to help others. I have a set of 8 equations. Each of the 8 equations are in terms of two variables. For example: x1 = f1(theta1, theta2) x2 = f2(theta1, theta2) x3 = f3(theta1, theta2) x4 = f4(theta1, theta2) y1 = f5(theta1, theta2) y2 = f6(theta1, theta2) y3 = f7(theta1, theta2) y4 = f8(theta1, theta2) the functions f_j are not neccesarily linear and are fairly complicated with many factors. I need to remove (eliminate) the theta1 and theta2 terms from the set and be left with a new set of equations that is in terms of x_i and y_i. I have tried using the "eliminate" function: eliminate({y2, x3, y1, x4, x1, x2, y3, y4}, {theta1, theta2}) and when I execute this command it provides no output, just skips to the next line. There is no error message or anything of the sort. Does anyone have any ideas or suggestions? Am I using eliminate incorrectly? Is there another command or method that I should try? I am relatively new to maple, but I understand enough to get by. I am using Maple 10 Build 190196. Thanks for any help you could provide.
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