Answer
$(-3,-4,-5)$
Work Step by Step
$2x+2y-3z=1$ Equation $(1)$
$y+2z=-14$ Equation $(2)$
$3x-2y=-1$ Equation $(3)$
Equation $(1)$ + Equation $(3)$
$(2x+2y-3z)+(3x-2y)=1+(-1)$
$5x-3z=0$ Equation $(4)$
$2\times$Equation $(2)$ - Equation $(1)$
$2(y+2z)-(2x+2y-3z)=2(-14)-1$
$(2y+4z)-(2x+2y-3z)=-28-1$
$-2x+7z=-29$ Equation $(5)$
$(2 \times$ Equation $(4))$ + $(5 \times$ Equation $(5))$
$2(5x-3z)+5(-2x+7z)=2(0)+5(-29)$
$(10x-6z)+(-10x+35z)=-145$
$29z=-145$
$z=-5$
Substitute $z=-5$ into Equation $(4)$ to get $x$.
$5x-3(-5)=0$
$5x+15=0$
$5x=-15$
$x=-3$
Substitute $x=-3$ into Equation $(3)$ to get $y$.
$3(-3)-2y=-1$
$-9-2y=-1$
$-2y=8$
$y=-4$
$(-3,-4,-5)$ satisfies the given equations.
Solution is $(-3,-4,-5)$
