Solve the following systems using Cramer's rule

Question

x+y+z=6

2x-y+z=3

3x-z=0

Answer 1

I'm using the determinant shortcut method for a 3x3 matrix where you append the first two columns to the right side of the matrix then subtract the right to left diagonal products sums from the left to right diagonal product sums.

A = X

Det A = 1+3+0+3+2-0 = 9

Replacing the first column with the X vector

x = (6+0+0-0+3-0)/9 = 9/9 = 1

Replacing the 2nd column with the X vector

y = (-3+18+0-9+12)/99 = 18/9 = 2

Replacing the 3rd column with the X vector

z = (0+9+0+18-0-0)/9 = 27/9 = 3