Which one of the following is not a basic solution of the system of linear equations x₁ + 2x₂ + x₃ = 4, 2x₁ + x₂ + 5x₃ = 5?

1. Ax₁ = −1, x₂ = 2, x₃ = 1
2. Bx₁ = 2, x₂ = 1
3. Cx₁ = 5, x₃ = −1
4. Dx₂ = 5/3, x₃ = 2/3

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. x₁ = −1, x₂ = 2, x₃ = 1

Explanation

With 2 equations and 3 variables, a basic solution sets one variable to 0. x₃ = 0 gives (2, 1); x₂ = 0 gives (5, −1); x₁ = 0 gives (5/3, 2/3). Option A has all three variables non-zero, so it is not basic.