Answer:
The answer to your question is x = 2, y = -1, z = 3
Step-by-step explanation:
Data
x + y + z = 4
x - 2y - z = 1
2x - y - 2z = -1
Solve the system of equations
| 1 1 1 |
| 1 -2 - 1 |
Δ = | 2 -1 -2| = (4 - 1 -2) - (-2 + 1 -4) = 1 + 5 = 6
| 1 1 1 |
| 1 -2 -1 |
| 4 1 1 |
| 1 -2 -1 |
Δx = |-1 -1 -2| = (16 - 1 + 1) - (-2 + 4 + 2) = 16 + 4 = 12
| 4 1 1 |
| 1 -2 -1 |
| 1 4 1 |
| 1 1 -1 |
Δy = | 2 - 1 -2 | = (-2 -1 -8) - (-8 + 1 + 2) = -11 - 5 = -6
| 1 4 1 |
| 1 1 -1|
| 1 1 4|
| 1 -2 1|
Δz = | 2 -1 -1| = (2 - 4 + 2) - (-1 -1 -16) = 0 + 18
| 1 1 4|
| 1 -2 1|
Find x, y and z
x = Δx/ Δ = 12/6 = 2
y = Δy/Δ = -6/6 = -1
z = Δz/Δ = 18/6 = 3
