1. **State the problem:** We need to find which system of equations has the solution $(1, 3, -1)$ for variables $(x, y, z)$. 2. **Recall the method:** To check if $(1, 3, -1)$ is a solution, substitute $x=1$, $y=3$, and $z=-1$ into each system's equations and verify if all equations hold true. 3. **Check system A:** - Equation 1: $x + y = 1 + 3 = 4$ ✓ matches right side 4 - Equation 2: $y - z = 3 - (-1) = 4$ but right side is 2 ✗ fails No need to check further; system A is not correct. 4. **Check system B:** - Equation 1: $x + 2y = 1 + 2(3) = 1 + 6 = 7$ ✓ matches right side 7 - Equation 2: $y + 2z = 3 + 2(-1) = 3 - 2 = 1$ ✓ matches right side 1 - Equation 3: $x - y - z = 1 - 3 - (-1) = 1 - 3 + 1 = -1$ ✓ matches right side -1 All equations hold true, so system B has the solution $(1, 3, -1)$. 5. **No need to check systems C and D since we found the correct system.** **Final answer:** System B has the solution $(1, 3, -1)$.