Real numbers x and y satisfy

Question

x + xy^2 = 250y,
x - xy^2 = -240y.
Enter all possible values of x, separated by commas.

Answer 1

first, just add the equations and you get
2x = 10y
x = 5y
now plug that in, and you have
5y + 5y^3 = 250y
5y^3 - 245y = 0
5y(y^2 - 49) = 0
y = -7, 0, 7
and x = 5y
now finish it off