Answer
(1, 4, 2)
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 2 and the second equation by 1 and add to obtain:
$8x -y =4 $
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:
$ 11x + y = 15 $
Plugging $y =8x -4 $ into this equation, we obtain:
$ 19x - 4 = 15 \\ x= 1$
Now, we plug this value into one of the equations that only has x and y in them to find:
$ y =4 $
Finally, we plug the values of x and y into the first equation listed in the book to find:
$ z = 2$
