Given
x² +y = 0
x³ -12x -y = 0
Find
the intersection point(s) (x, y)
Solution
Add the two equations together, then factor.
... (x² +y) + (x³ -12x -y) = 0 + 0
... x³ +x² -12x = 0
... x(x +4)(x -3) = 0
Then x = {0, -4, 3}.
The corresponding y-values are
... y = -x² = {0, -16, -9}
The points of intersection are (-4, -16), (0, 0), (3, -9)
