Answer:
D = -13, Dx = 13, and Dy = -78
Explanation:
To solve the system of equations using determinants, we need to first set up the coefficient matrix and the constant matrix. The coefficient matrix is formed by the coefficients of the variables, and the constant matrix is formed by the constants on the right-hand side of the equations.
The coefficient matrix for this system is:
```
3 5
2 -1
```
The constant matrix is:
```
27
-8
```
We can now use these matrices to find the values of D, Dx, and Dy.
D is the determinant of the coefficient matrix:
```
| 3 5 |
| 2 -1 |
D = (3 * -1) - (5 * 2)
D = -3 - 10
D = -13
```
Dx is found by replacing the x-coefficients in the coefficient matrix with the constants from the constant matrix:
```
| 27 5 |
| -8 -1 |
Dx = (27 * -1) - (5 * -8)
Dx = -27 + 40
Dx = 13
```
Dy is found by replacing the y-coefficients in the coefficient matrix with the constants from the constant matrix:
```
| 3 27 |
| 2 -8 |
Dy = (3 * -8) - (27 * 2)
Dy = -24 - 54
Dy = -78
```
Therefore, D = -13, Dx = 13, and Dy = -78.
To find x and y, we can use Cramer's rule:
```
x = Dx / D
y = Dy / D
x = 13 / (-13)
x = -1
y = (-78) / (-13)
y = 6
```
So the solution to this system of equations is x = -1 and y = 6.