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Step 2) Factor the cubic
Let P(x) = x^3 - 19x + 30

According to rational root theorem, the only rational root possible is
(x +- 30), (x +- 15), (x +- 10), (x +- 5), (x +- 3), (x +- 2), (x +- 1)
According to polynomial factor theorem, if P(a) = 0, then (x - a) is a root.
We try all the possible rational factor.
P(-5) = P(2) = P(3) = 0
We can conclude that P(x) = (x + 5)(x - 2)(x - 3)

Step 3) Finding x and y
x^3 - 19x + 30 = 0
(x + 5)(x - 2)(x - 3) = 0
x = -5 or x = 2 or x = 3

Now, find y by substituting x to equation 2.
x = -5 => y = -5
x = 2 => y = 2
x = 3 => y = 1/3

The solutions are (x,y) = {(-5, -5), (2, 2), (3, 1/3)}

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Step 1) Substitute y

Step 2) Factor the cubic Let P(x) = x^3 - 19x + 30

Step 3) Finding x and y x^3 - 19x + 30 = 0 (x + 5)(x - 2)(x - 3) = 0 x = -5 or x = 2 or x = 3

The solutions are (x,y) = {(-5, -5), (2, 2), (3, 1/3)}

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