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Solve using augmented matrix methods. Use a graphing calculator to perform the row op 0.16x₁ + 4.35x₂ = 6...

Solve using augmented matrix methods. Use a graphing calculator to perform the row op
0.16x₁ + 4.35x₂ = 6
6.25x₁ + 4.37x₂ = 8
Select the correct choice below and, if necessary, fill in the answer box to complete your choi
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

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

\[ \begin{bmatrix} 0.16 & 4.35 & | & 6 \\ 6.25 & 4.37 & | & 8 \end{bmatrix} \]

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

\[ \begin{bmatrix} 1 & 0 & | & 1.1429 \\ 0 & 1 & | & 1.2857 \end{bmatrix} \]

Thus, the unique solution is:

  1. A. The unique solution is x₁ = 1.1429 and x₂ = 1.2857 (rounded to four decimal places).

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