Final answer:
The solution set of the system of equations given the determinants D=-27, Dx=0, Dy=81, and Dz=-54 is (x, y, z) = (0, -3, 2), using Cramer's rule to find the values of x, y, and z.
Step-by-step explanation:
The question provided is concerning a system of linear equations typically found in the subject of Mathematics. Specifically, it relates to Cramer's rule and solving systems of linear equations using determinants. Given the information D=-27, Dx=0, Dy=81, and Dz=-54, we can use these determinants to solve for the unknowns x, y, z in a system of three linear equations.
According to Cramer's rule, the solution set of the system will be:
- x = Dx / D
- y = Dy / D
- z = Dz / D
Plugging in the given values into these formulas results in:
- x = 0 / -27 = 0
- y = 81 / -27 = -3
- z = -54 / -27 = 2
Thus, the solution set for the system of equations is (x, y, z) = (0, -3, 2).