#### Answer

(3, 5, 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 4 and the second equation by -3 and add to obtain:
$-2x +10y = 44 $
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 2 and the third equation by -3 and add to obtain:
$ -7x + 2y = -11 $
Plugging $x = 5y -22$ into this equation, we obtain:
$-33y + 154 = -11 \\ y =5$
Now, we plug this value into one of the equations that only has x and y in them to find:
$ x = 3$
Finally, we plug the values of x and y into the first equation listed in the book to find:
$ z = 1$