Can you show me how to use determinants to solve these?(show steps pls)?

Question

4x + 2y - z = 9
2x + y = 4
x + 2y - 2z = 2

Answer 1

Write the equations (or you may jump over this step) as:
4x + 2y - 1z = 9
2x + 1y + 0z =4
1x + 2y - 2z =2
So the determinant of the co-efficient is:
| 4 2 -1|
| 2 1 0|
| 1 2 -2|
Subtracting twice the first row to the third row, and expand with the third colume to get:
| 4 2 -1|
| 2 1 0| = -3
| -7 -2 0|
Replace the x-coefficient with the constant vector in the determinant of the co-efficient to get:
| 9 2 -1|
| 4 1 0|
| 2 2 -2|
which may be calculated in the same way to get:
| 9 2 -1|
| 4 1 0| = -8
|-16 -2 0|
Replace the y-coefficient with the constant vector in the determinant of the co-efficient to get:
| 4 9 -1|
| 2 4 0|
| 1 2 -2|
which may be calculated in the same way to get:
| 4 9 -1|
| 2 4 0| = 4
|-7 -16 0|
Do the same thing for z:
| 4 2 9|
| 2 1 4|
| 1 2 2|
Now subtracting twice of the the first colume from the third colume to get:
| 4 2 1|
| 2 1 0| = 3
| 1 2 0|
Hence x = -8/(-3) = 8/3
y = 4/(-3) = -4/3
z = 3/(-3) = -1