Problem
Using the given matrix in reduced row echelon form, determine the solution of the corresponding system of linear equations. Then enter the solution* of $x$ in the box. *If there is a free variable, set $z=t$ and if the system is inconsistent type "inconsistent" in the box. \[ \left[\begin{array}{ccc|c} 1 & 0 & 7 & 4 \\ 0 & 1 & -9 & 5 \\ 0 & 0 & 0 & 1 \end{array}\right] \]
Solution
Step 1 ：The given matrix is in reduced row echelon form. This form corresponds to the system of linear equations: \[\begin{align*} x + 7z &= 4 \\ y - 9z &= 5 \\ 0 &= 1 \end{align*}\]
Step 2 ：The third equation, 0 = 1, is a contradiction, which means the system of equations is inconsistent. Therefore, there is no solution for x.
Step 3 ：Final Answer: \(\boxed{\text{The system is inconsistent}}\)
