Solve the system by any method. \[ \begin{array}{r}x+y-z=-17 \\ 2 x-y+z=2\end{array} \] Select the correct choice and, if necessary, fill in any answer boxes within your choice. A. There is one solution. The solution set is ( (Simplify your answers.) B. There are infinitely many solutions. The solution set is \( (\square, \square, z) \), where \( z \) is any real number. (Simplify your answers. Use integers or fractions for any numbers in the expressions.) C. There is no solution.

To solve the system of equations: 1. Start with the two equations: \[ x + y - z = -17 \quad \text{(1)} \] \[ 2x - y + z = 2 \quad \text{(2)} \] 2. Rearranging equation (1) for \( z \): \[ z = x + y + 17 \quad \text{(3)} \] 3. Substitute equation (3) into equation (2): \[ 2x - y + (x + y + 17) = 2 \] Simplifying this gives: \[ 3x + 17 = 2 \quad \Rightarrow \quad 3x = -15 \quad \Rightarrow \quad x = -5 \] 4. Substitute \( x = -5 \) back into equation (3): \[ z = -5 + y + 17 \quad \Rightarrow \quad z = y + 12 \quad \text{(4)} \] 5. Substitute \( x = -5 \) into equation (1) to find \( y \): \[ -5 + y - z = -17 \quad \Rightarrow \quad y - z = -12 \quad \Rightarrow \quad z = y + 12 \quad \text{(which matches equation (4))} \] From equation (4), we conclude \( z \) depends on \( y \). Hence, we have infinite solutions and can express the solution set as: \[ \text{Solution Set: } (-5, y, y + 12) \text{ where } y \text{ is any real number.} \] So, the correct choice is: B. There are infinitely many solutions. The solution set is \( (-5, y, y + 12) \), where \( y \) is any real number.