Final answer:
The available information does not provide enough context to determine which of the options -18, 0, 18, or -27 is the correct determinant for a set of linear equations. The determinant is specific to the matrix of coefficients from the system of equations.
Step-by-step explanation:
The student's question seems to be asking about the determinant for a set of linear equations; however, the information provided does not directly relate to the determinant of a matrix or a set of linear equations. To find the determinant of a matrix, one would need the actual matrix of coefficients from the system of linear equations. Determinants are used to solve systems of linear equations, among other things, and they are specific to square matrices.
Nonetheless, without a specific matrix to reference, we cannot accurately select an option from a), b), c), or d) as the determinant. If the student can provide the matrix of coefficients from their system, we would calculate the determinant by applying the appropriate formula, which involves multiplying and subtracting the products of the diagonals for a 2x2 matrix, or using more complex methods for larger matrices.