Final answer:
To solve the system of equations using Cramer's method, determine the determinant of the coefficient matrix and the determinants with each variable's column replaced by the constants. Calculate the values of x, y, and z using specific determinants divided by the main determinant.
Step-by-step explanation:
To solve the system of equations using Cramer's method, we need to calculate the determinant (D) of the coefficient matrix and the determinants of matrices obtained by replacing one column by the column of constants. The system given is:
3x + 8y - 5z = 6
x + y + z = 3
2x - 5y + 5z = 2
Step 1: Find the determinant of the coefficient matrix (D).
Step 2: Find Dx, which is the determinant of the matrix formed by replacing the x column with the constant column.
Step 3: Find Dy, which is the determinant of the matrix formed by replacing the y column with the constant column.
Step 4: Find Dz, which is the determinant of the matrix formed by replacing the z column with the constant column.
Finally, you solve for the variables using the formulas x = Dx / D, y = Dy / D, and z = Dz / D.
This procedure involves many algebraic steps and you'll need to carefully calculate each determinant to find the values of x, y, and z.