\( \left. \begin{array} { l l } { x - 4 = 10 } & { \frac { 1 } { 3 } x = 12 } \\ { x ^ { 3 } = 12 } \end{array} \right. \)

Solve the system of equations by following steps: - step0: Solution: \(\left\{ \begin{array}{l}x-4=10\\\frac{1}{3}x=12\\x^{3}=12\end{array}\right.\) - step1: Calculate: \(\left\{ \begin{array}{l}x=14\\x=36\\x=\sqrt[3]{12}\end{array}\right.\) - step2: Find the intersection: \(x \in \varnothing \) The system of equations provided is: 1. \( x - 4 = 10 \) 2. \( \frac{1}{3} x = 12 \) 3. \( x^{3} = 12 \) Upon solving these equations, we find that there are no common solutions among them, which means the solution set is empty: \[ x \in \varnothing \] This indicates that there are no values of \( x \) that satisfy all three equations simultaneously.