#### Answer

(-1, 3, 1)

#### Work Step by Step

In order to solve systems of three linear equations, we multiply the first and second equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by 1 and the second equation by -4 and add to obtain:
$-18x +9y = 45$
We now multiply the first and third equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by one and the third equation by 2 and add to obtain:
$ 8x +7y = 13 $
Plugging $x = .5y -2.5$ into this equation, we obtain:
$ 11y -20 = 13 \\ y =3 $
Now, we plug this value into one of the equations that only has x and y in them to find:
$ x = -1$
Finally, we plug the values of x and y into the first equation listed in the book to find:
$ z = 1$