Answer
$(-4,2,-1)$
Work Step by Step
Given Equations,
$3x-y+z=-15$ Equation $(1)$
$x+2y-z=1$ Equation $(2)$
$2x+3y-2z=0$ Equation $(3)$
Add Equation $(1)$ and Equation $(2)$
$3x-y+z+x+2y-z=-15+1$
$4x+y=-14$ Equation $(4)$
Multiply Equation $(1)$ by $2$ and add with Equation $(3)$
$2(3x-y+z)+2x+3y-2z=2(-15)+0$
$6x-2y+2z+2x+3y-2z=-30$
$8x+y=-30$ Equation $(5)$
Subtract Equation $(4)$ from Equation $(5)$
$8x+y-(4x+y)=-30-(-14)$
$8x+y-4x-y=-30+14$
$4x=-16$
$x=-4$
Substituting $x$ value in Equation $(5)$
$8x+y=-30$
$8(-4)+y=-30$
$-32+y=-30$
$y=-30+32$
$y=2$
Substituting $x$and $y$ value in Equation $(1)$
$3x-y+z=-15$
$3(-4)-(2)+z=-15$
$-12-2+z=-15$
$-14+z=-15$
$z=-15+14$
$z=-1$
Solution $(-4,2,-1)$
