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Solve using augmented matrix methods. Use a graphing calculator to perform the row operations 0.8x₁ +...

Solve using augmented matrix methods. Use a graphing calculator to perform the row operations
0.8x₁ + 4.32x₂ = 2
1.25x₁ + 6.19x₂ = 8
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 = ___ (Round to four decimal places as needed)
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:

[ 0.8 4.32 | 2 ]
[ 1.25 6.19 | 8 ]

Using a graphing calculator or performing row operations manually, we find the reduced row-echelon form:

[ 1 0 | 1.5 ]
[ 0 1 | 0.25 ]

This corresponds to the equations:

x₁ = 1.5
x₂ = 0.25

Answer: The unique solution is x₁ = 1.5000 and x₂ = 0.2500.

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