#### Answer

2$x$- $y$ + 3$z$ =13
$x$ + $y$ - $z$ = -2
3$x$ + 2$y$ + 2$z$ = 13
(1, 1, 4)
$x$ = 1
$y$ = 1
$z$ = 4

#### Work Step by Step

Step 1: Write Out Problems
2$x$- $y$ + 3$z$ =13 (equation 1)
$x$ + $y$ - $z$ = -2 (equation 2)
3$x$ + 2$y$ + 2$z$ = 13 (equation 3)
Step 2: Find the 2 equations with like terms (in this case $y$), and cancel out the like terms
2$x$- $y$ + 3$z$ =13
$x$ + $y$ - $z$ = -2
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3$x$ + 2$z$ = 11 (equation 4)
Step 3: Add two $other$ equations and eliminate $y$ again
2(2$x$- $y$ + 3$z$) =13 (2)
3$x$ + 2$y$ + 2$z$ = 13
Simplify:
$4x$- $2y$ + $6z$ = 26
3$x$ + 2$y$ + 2$z$ = 13
____________________
$7x$ + $8z$ = 39 (equation 5)
Step 4: Combine equations 4 and 5, and multiply equation 4 by -4
-4 ($3x$ + $2z$) = 11 (-4)
$7x$ + $8z$ = 39
Simplify:
$-12x$ -$8z$ = -44
$7x$ + $8z$ = 39
$-5x$ = -5
$x$ = 1
Now replace $x$ with 1
3(1) + $2z$ = 11
$2z$ = 8
$z$ = 4
Solve: for $y$
$x$ + $y$ - $z$ = -2
1 + $y$ - 4 = -2
$y$ -3 = -2
$y$ = 1