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

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.