Problem

Question 17
\( 1 \mathrm{pts} \)
Which of the following classifications fits the system \( \left\{\begin{array}{l}y=3 x+4 \\ x+3 y=6\end{array}\right. \) ?
consistent and independent
consistent and dependent
inconsistent and independent
inconsistent and dependent

Answer

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Answer

Step 3: Since the determinant is not 0, the system is consistent and independent.

Steps

Step 1 ：Step 1: Rewrite the system in matrix form: \( \begin{bmatrix} -3 & 1 \\ 1 & 3 \end{bmatrix}\begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -4 \\ 6 \end{bmatrix} \)

Step 2 ：Step 2: Find the determinant: \(\mathrm{Det} = (-3)(3) - (1)(1) = -8 \)

Step 3 ：Step 3: Since the determinant is not 0, the system is consistent and independent.

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