#### Answer

The system of equations has no solution.

#### Work Step by Step

Let us consider the first inequality and put a test point $\left( 0,0 \right)$ in this inequality to check whether it satisfies the inequality or not as given below:
$\begin{align}
& y\ge 6x-24 \\
& 0\ge 0-24 \\
& 0\ge -24 \\
\end{align}$
Which is correct. Thus, the test point $\left( 0,0 \right)$ satisfies the inequality and the shaded region will be towards the origin.
Also, consider the second inequality and put a test point $\left( 0,0 \right)$ in this inequality to check whether it satisfies the inequality or not as given below:
$\begin{align}
& y\lt6x-24 \\
& 0\lt0-24 \\
& 0\lt -24 \\
\end{align}$
Which is false.
Thus, there is no solution.