+0

0
105
2

Real numbers x and y satisfy

\begin{align*} x + xy^2 &= 250y, \\ x - xy^2 &= -240y. \end{align*}

Enter all possible values of x separated by commas.

Mar 30, 2021

#1
0

Elimnating y, we get x^2 = 1225.  So the possible values of x are 35 and -35.

Mar 30, 2021
#2
+121004
+1

x + xy^2  =    250y

x -  xy^2  =  - 240y         add  these

2x  = 10y

x = (10/2) y

x = 5y                 sub this  back  into the first equation

5y + 5yy^2 = 250y           divide  though by 5y

1 + y^2  =  50

y^2  = 49               take both roots

y =    -7            or     y  =  7

x = 5(-7)  =  -35               x = 5(7)  =  35

And   (x, y)  =  (0,0)  is a trivial solution

So

x =  35, 0 , 35

Mar 30, 2021
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