Answer
$(3,-3,1)$
Work Step by Step
$x+y-z=-1$ Equation $(1)$
$-4x-y+2z=-7$ Equation $(2)$
$2x-2y-5z=7$ Equation $(3)$
Add Equation $(1)$ and Equation $(2)$
$x+y-z-4x-y+2z=-1-7$
Combine like terms.
$-3x+z=-8$ Equation $(4)$
Multiply Equation $(2)$ by $-2$ and add with Equation $(3)$
$-2(-4x-y+2z)+2x-2y-5z = -2(-7)+7$
$8x+2y-4z+2x-2y-5z=14+7$
Combine like terms.
$10x-9z=21$ Equation $(5)$
Multiply Equation $(4)$ by $9$ and add with Equation $(5)$
$9(-3x+z)+10x-9z=9(-8)+21$
$-27x+9z+10x-9z=-72+21$
Combine like terms.
$-17x=-51$
$x = 3 $
Substitute $x$ value in Equation $(4)$
$-3x+z=-8$
$-3(3)+z=-8$
$-9+z=-8$
$z=-8+9$
$z=1$
Substitute $x$ and $z$ values in Equation $(1)$
$x+y-z=-1$
$3+y-1=-1$
$2+y=-1$
$y=-3$
$(3,-3,1)$ satisfies the given three equations.
The solution is $(3,-3,1)$
