#### Answer

(3, 0, -2)

#### Work Step by Step

In order to solve systems of three linear equations, we 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 1 and the third equation by -4 and add to obtain:
$-7x -17y = -21 $
We now 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 one and the second equation by two and add to obtain:
$ 7x + y = 21 $
Plugging $7x =-17y + 21$ into this equation, we obtain:
$-16y +21 = 21 \\ y = 0 $
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 = -2$