Suppose that the augmented matrix of a system of linear
$$\left[\begin{array}{cccc}1& 0& -4& \frac{23}{3}\\ 3& 1& -10& 27\\ 0& 4& 8& 16\end{array}\right].$$

Solve the system and provide the information requested.
The system has:
a unique solution
which is
$$x=◻y=◻z=◻$$
infinitely many solutions
two of which are
$$\begin{array}{lll}x=◻& y=◻& z=◻\\ x=◻& y=◻& z=◻\end{array}$$
no solution

Step 1 ：Suppose that the augmented matrix of a system of linear equations is given as follows: $$\left[\begin{array}{cccccccccc}1& 0& -4& \frac{23}{3}3& 1& -10& 270& 4& 8& 16\end{array}\right].$$

Step 2 ：Let's define the equations based on the augmented matrix: $$\begin{array}{rlrl}x-4z& =\frac{23}{3}3x+y-10z& =274y+8z& =16\end{array}$$

Step 3 ：Solving the system of equations, we find that the solution is parametric in terms of $z$. This means that there are infinitely many solutions to the system, and we can generate specific solutions by choosing specific values for $z$.

Step 4 ：For example, if we choose $z=0$, we get $x=7.67$ and $y=4$. If we choose $z=1$, we get $x=11.67$ and $y=2$.

Step 5 ：$\boxed{{\displaystyle \text{Final Answer: The system has infinitely many solutions. Two of them are:}}}$

Step 6 ：$$\begin{array}{lllll}x=7.67& y=4& z=0x=11.67& y=2& z=1\end{array}$$