Solve the system of equations. \[ \begin{array}{r}x+5 y-z=24 \\ y+6 z=41 \\ z=6\end{array} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete the choice. A. The solution of the given system is \( x=\square, y=\square \), and \( z=\square \). (Simplify your answers.) B. The system has infinitely many solutions. If \( z \) is any real number, then \( x=\square \) and \( y=\square \). (Type expressions using \( z \) as the variable.)

To solve the system of equations, we start with the given equations: 1. \( x + 5y - z = 24 \) 2. \( y + 6z = 41 \) 3. \( z = 6 \) First, we substitute \( z = 6 \) into the second equation: \[ y + 6(6) = 41 \] \[ y + 36 = 41 \] \[ y = 41 - 36 \] \[ y = 5 \] Now that we have \( y = 5 \) and \( z = 6 \), we substitute these values into the first equation to find \( x \): \[ x + 5(5) - 6 = 24 \] \[ x + 25 - 6 = 24 \] \[ x + 19 = 24 \] \[ x = 24 - 19 \] \[ x = 5 \] Now we have the values for \( x \), \( y \), and \( z \): \[ x = 5, \quad y = 5, \quad z = 6 \] Thus, the solution of the given system is: A. The solution of the given system is \( x=5, y=5 \), and \( z=6 \).