Answer
$x$ = 0, $y$ = 4, $z$ =-2
Work Step by Step
$x$ + $y$ + $z$ = 2
-$x$ + 3$y$ + 2$z$ = 8
4$x$ + $y$ = 4
$R_{1}$+$R_{2}$→$R_{2}$
$x$ + $y$ + $z$ = 2
4$y$ + 3$z$ = 10
4$x$ + $y$ = 4
-4$R_{1}$+$R_{3}$→$R_{3}$
$x$ + $y$ + $z$ = 2
4$y$ + 3$z$ = 10
-3$y$ - 4$z$ = -4
3$R_{2}$→$R_{2}$
4$R_{3}$→$R_{3}$
$x$ + $y$ + $z$ = 2
12$y$ + 9$z$ = 30
-12$y$ - 16$z$ = -16
$R_{2}$+$R_{3}$→$R_{3}$
$x$ + $y$ + $z$ = 2
12$y$ + 9$z$ = 30
-7$z$ = -14
$z$ = -2, plug this value into (12$y$ + 9$z$ = 30)
12$y$ + 9(-2) = 30
$y$ = 4
$x$ + (4) + (-2) = 2
$x$ = 0
