Answer: x = {0, 35, -35}
Step-by-step explanation:
Add the two equations together to eliminate the xy² term.
x + xy² = 250y
+ x - xy² = -240y
2x = 10y
÷2 ÷2
x = 5y
Substitute x = 5y into either of the equations to solve for "y".
5y + 5y(y²) = 250y
5y + 5y³ = 250y
5y³ + 5y - 250y = 0
5y³ - 245y = 0
5y(y² - 49) = 0
5y = 0 y² - 49 = 0
y = 0 y = ±7
Substitute y = 0, y = 7, and y = -7 into either of the equations to solve for "x".
x + x(0)² = 250(0) x + x(7)² = 250(7) x + x(-7)² = 250(-7)
x + 0 = 0 x + 49x = 1750 x + 49x = -1750
x = 0 50x = 1750 50x = -1750
x = 35 x = -35
