Solve the given linear system using Gaussian elimination. Which of the following options correctly represents the values of x₁, x₂, and x₃?

a) x₁ = 2, x₂ = 1, x₃ = 3
b) x₁ = 3, x₂ = -1, x₃ = 2
c) x₁ = -1, x₂ = 2, x₃ = 3
d) x₁ = 1, x₂ = -2, x₃ = 3