Question

Find the solution of this system of equations algebraically.
(A) y = -x
(B) y = x3 + 3x2 + 2x

(0, 0)
(0, -1) and (0, -2)
(0, 0), (-1, 1) and (-2, 2)
(-1, 1) and (-3, 3)
It has no solution.

Answer 1

@Michele_Laino

Answer 2

If we apply the elimination method, we can write:
\[\Large \begin{gathered}
- x = y = {x^3} + 3{x^2} + 2x \hfill \\
{x^3} + 3{x^2} + 3x = 0 \hfill \\
x\left( {{x^2} + 3x + 3} \right) = 0 \hfill \\
\end{gathered} \]

Answer 3

x=0

Answer 4

It also has complex roots

Answer 5

yes! Nevertheless we have to understand if there are other solutions or there are not

Answer 6

ok!

Answer 7

so what is the right option?

Answer 8

ugh the one with no solution?

Answer 9

we have only one real solution

Answer 10

namely x=0, y=0

Answer 11

yea

Answer 12

thanks!

Answer 13

thanks! :)