Question

Please help! I know I should know how to do this but I cant seem to figure it out. Solve for x&y
5x^4y+y^5+y=0
x^5+x5y^4+x=0

Answer 1

My first thougths (and my 2 cents):

I'd rewrite the equations as\[y^{5}+5x^{4}y+y=0\]\[x^{5}+5y^{4}x+x=0\]
These have a nice parallel structure which implies to me that x and y are interchangable...or, in other words, x=y.

Since all the terms are the same sign (only + are used), the only way you can get zero given x=y is for x=y=0.

THis solution works...but I'm not sure if it's the only solution...but given the parallel structure of the two equations, it seems likely that this is the only real solution.

Answer 2

Thank you so much! thats what i thought just was trying to show how I came to that conclusion but it appears that it just is

Answer 3

lol :) sometimes "It just is" is all you need :)

Answer 4

:) thxs