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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!

Respuesta :

joseaaronlara

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

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