# Solve the following using Cramer's Rule: 8x-4y+7z=34 5x+6y+3z=-21 3x+7y-8z=-85

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According to Cramer's Rule we can write the given set of equations in the matrix form as follows:

| 8 -4 7 | | x | | 34 |

| 5 6 3 | | y | = |-21 |

| 3 7 -8 | | z | |-85 |

Now the value of the determinant for the matrix

| 8 -4 7 |

| 5 6 3 |

| 3 7 -8 |

is -629, let us name this as D

x is given by

| **34** -4 7|

|**-21** 6 3|

|**-85** 7 -8 |

divided by D

The value of the determinant of

| **34** -4 7|

|**-21** 6 3|

|**-85** 7 -8 |

is 1887. Therefore x = 1887/ -629 = -3

Similarly

y is given by

| 8 **34** 7 |

| 5 **-21** 3 |

| 3 **-85** -8 |

divided by D

The value of the determinant of

| 8 **34** 7 |

| 5 **-21** 3 |

| 3 **-85** -8 |

is 2516. Therefore y = 2516/ -629 = -4

z is given by

| 8 -4 **34** |

| 5 6 **-21**|

| 3 7 **-85** |

divided by D

The value of the determinant of

| 8 -4 **34** |

| 5 6 **-21**|

| 3 7 **-85** |

is -3774. Therefore z = -1525/ -629 = 6

**Therefore x = -3, y= -4 and z= 6.**