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Solve using augmented matrices. 3x₁ + x₂ = 5 x₁ - x₂ = -1 Select the correct choice below and, if...

Solve using augmented matrices.
3x₁ + x₂ = 5
x₁ - x₂ = -1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The unique solution is x₁ = □ and x₂ = □
B. The system has infinitely many solutions. The solution is x₁ = □ and x₂ = t (Simplify your answer. Type an expression using t as the variable)
C. There is no solution

Answer

A. The unique solution is x₁ = 1 and x₂ = 2.

The augmented matrix for the system is:

  1. [3 1 | 5]
  2. [1 -1 | -1]

Perform row operations to solve:

  1. R2 = R2 - (1/3)R1: [3 1 | 5], [0 -4/3 | -8/3]
  2. R2 = -3/4 * R2: [3 1 | 5], [0 1 | 2]
  3. R1 = R1 - R2: [3 0 | 3], [0 1 | 2]
  4. R1 = (1/3)R1: [1 0 | 1], [0 1 | 2]

Thus, the solution is x₁ = 1 and x₂ = 2.

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