Answer
$(-1,5,2)$
Work Step by Step
$x-y+z = -4$ Equation $(1)$
$3x+2y-z = 5$ Equation $ (2)$
$-2x+3y-z = 15$ Equation $(3)$
Add Equation $(1)$ and $(2)$ to eliminate $z$
$4x+y = 1$ Equation $(4)$
Add Equation $(1)$ and $(3)$ to eliminate $z$
$-x+2y = 11 $ Equation $(5)$
Add $(4)$ and $ 4 \times (5)$ to eliminate $x$ and get $y$
$4x -(4)x +y +(4)2y = 1+ (4)11$
$4x -4x +y +8y = 1+ 44$
$9y = 45$
$y=5$
Substituting $y$ value in Equation $(4)$ to get $x$
$4x+y = 1$
$4x+5= 1$
$4x = 1-5$
$4x = -4$
$x = -1$
Substituting $x $ and $y$ values in Equation $(1)$ to get $z$
$x-y+z = -4$
$-1-5+z = -4$
$-6+z = -4$
$z = -4+6$
$z= 2$
$x = -1$
$y=5$
$z= 2$
Solution is $(-1,5,2)$
