If you count the terms starting with 0 instead of 1, 
there are n terms, and the kth term is 

In the expansion of (x+y)n, the second term is 1620.

That's the first term if you start counting with 0,  So





the third term is 4320

That's the second term if you start counting with 0,  So



 

 

and the fourth term is 5760,

That's the third term if you start counting with 0,  So









Divide equal by equals. That is,

Divide the sides of the 2nd equation by the sides of the 1st equation



Simplify by canceling and subtracting exponents:





Divide the sides of the 3rd equation by the sides of the 2nd equation



Simplify by canceling and subtracting exponents:





Setting the expressions for  equal



multiply through by 16







Taking the first two equations of the system:







Solve the 1st equation for y


Substitute in the 2nd








Substitute in





So x=3, y=4, n=5 

Edwin