Real numbers $x$ and $y$ satisfy \begin{align*} x + xy^2 &= 250y, \\ x - xy^2 &= -240y. \end{align*}
+128566 x + xy^2 = 250y
x - xy^2 = - 240 y add these
2x = 10y
x = (10 / 2) y
x = 5y sub the into the first equation for x
5y + 5y * y^2 = 250 y divide through by 5
y + y^3 = 50y
y^3 - 49y = 0
y ( y^2 - 49) = 0
y ( y + 7) (y - 7) = 0
Solutions for y =
0 , - 7 , 7
So
x = 5(0) = 0
x = 5(-7) = -35
x =5(7) = 35
So....the solutions are (x, y) = (0,0 ) (-7, -35) (7, 35)
