\[ \begin{aligned} 9 x-y & =-4 \\ -8 x-2 y & =7 \end{aligned} \] Answer Attempt 1 out of 2 Write the three relevant determinants in any order: \( \square \) , \( \square \) , \( \square \)

To solve the system of equations, we can represent the equations as a matrix and calculate the determinants relevant for solving it. The coefficient matrix \( A \) is: \[ \begin{bmatrix} 9 & -1 \\ -8 & -2 \end{bmatrix} \] The determinant of \( A \) is calculated as follows: \[ \text{det}(A) = (9)(-2) - (-1)(-8) = -18 - 8 = -26. \] The first determinant you can find (often called \( D \)) is \( \text{det}(A) = -26 \). Next, we derive determinants for the modified matrices formed by including the constant terms. Here’s one: The determinant with y replaced (commonly called \( D_y \)) is: \[ \begin{bmatrix} 9 & -4 \\ -8 & 7 \end{bmatrix} \] Calculating, we get: \[ D_y = (9)(7) - (-4)(-8) = 63 - 32 = 31. \] Finally, the determinant with x replaced (commonly called \( D_x \)) is: \[ \begin{bmatrix} -4 & -1 \\ 7 & -2 \end{bmatrix} \] Calculating, we have: \[ D_x = (-4)(-2) - (-1)(7) = 8 + 7 = 15. \] So, the three relevant determinants are: \( -26 \), \( 31 \), \( 15 \).