Use Matrices to Solve the System of Equations (If Possible) $\left\{ \begin{aligned}- 2 x - y - 7 z & = - 27 \\x - 5 y + z & = - 24 \\- 2 x + 4 y - 7 z & = - 2\end{aligned} \right.$

Use matrices to solve the system of equations (if possible) . Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $\left\{ \begin{aligned}- 2 x - y - 7 z & = - 27 \\x - 5 y + z & = - 24 \\- 2 x + 4 y - 7 z & = - 2\end{aligned} \right.$

A) x = 3, y = -5, z = 4
B) x = -3, y = -5, z = 4
C) x = -3, y = 5, z = 4
D) x = 5, y = 3, z = -4
E) no solution