Question

2. Solve the following system of equations

x+y+z=4
x − 2y − z = 1
2x − y − 2z = −1

Select the appropriate response:
A) x =3, y = −3, z = 3
B) x = 2, y = −1, z = 3
C) x = 2, y = −21, z = 3
D) None of the above

Help please!

Answer 1

The answer to your question is x = 2, y = -1, z = 3

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