Considering the following equations:

3x - 2y + 5z = 14

-x + 3y + z = 8

5x - y - 5z = -12

We can created the augmented matrix:

(1)To make the '3' in the (1,1) entry our pivot we convert it to 1 by

doing the following:

R1 = 1/3R1

(2)Next we make entry (2,1) equal to zero by:

R2 = 5R2 + R3

(3)Now to make entry (3,1) zero we do:

R3 = -5R1 + R3

(4)Finally, to make entry (3,2) also equal to

zero we perform:

R3 = R2 + -6R3

(5)As you can see we now have a triangular matrix in which

'z' can be solved easily:

80z = 240

z = 3

Also R2 can be solved to find the value of 'y':

14y = 28

y = 2

And lastly using substitution we can find the

value of 'x':

x - (2/3)(2) + (5/3)(3) = (14/3)

x - (4/3) + (15/3) = (14/3)

x + (11/3) = (14/3)

x = 1

Thus having all of our answers:

x = 1

y = 2

z = 3