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.
+128631 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
