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For each of the following, solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, say so and explain why. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.
x₁ + 2x₂ - x₃ = -6
2x₁ + x₂ + x₃ = 3
3x₁ + 3x₂ + 2x₃ = -3
x₁ - 3x₂ + x₃ = 13

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