\[
\begin{array}{l}
x+2 y-3 z=2 \\
x-3 y-z=3 \\
-x+3 y+(4-k) z=7
\end{array}
\]
If we don't apply the Cramer's method to the given linear system then find the value for $k$.
Eliminate y from the new equations to find the value of k: \(\boxed{k = \frac{-2x + 16y + z - 2}{z}}\)
Step 1 :Eliminate x from the first two equations and then from the second and third equations to get two new equations: \(5y - 2z = -1\) and \(2x - 6y - z(4 - k) - z = -4\)
Step 2 :Eliminate y from the new equations to find the value of k: \(\boxed{k = \frac{-2x + 16y + z - 2}{z}}\)