Three variables, non-linear system of equations

[Roger.Robert]

How do I solve this system of equations?

\(\displaystyle \begin{align*} xyz &= -24\, \\
xy+xz+yz &= -14 \\
x+y+z &= \,1
\end{align*}
\)

 

[Deleted member 4993]

How do I solve this system of equations?

\(\displaystyle \begin{align*} xyz &= -24\, \\
xy+xz+yz &= -14 \\
x+y+z &= \,1
\end{align*}
\)

Hint:

x(y+z) + yz = -14

y + z = 1-x

yz = - 24/x

Continue....