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Solve using augmented matrix methods. -4x₁ + 5x₂ = 9 -12x₁ + 15x₂ = -4 Select the correct choice below and...

Solve using augmented matrix methods.
-4x₁ + 5x₂ = 9
-12x₁ + 15x₂ = -4
Select the correct choice below and fill in any answer boxes in your choice.
A. The unique solution is x₁ = [ ] and x₂ = [ ] (Simplify your answer.)
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

To solve the system using augmented matrix methods, we first write the augmented matrix:

Augmented Matrix:

[ -4  5 |  9 ]
[ -12 15 | -4 ]

We perform row operations to simplify:

  1. Multiply the first row by 3 and add to the second row to eliminate x₁ from the second equation:
[ -4  5 |  9 ]
[ 0 0 | 23 ]

The second row becomes 0 = 23, which is a contradiction.

Conclusion: The system has no solution.

Answer: C. There is no solution.

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