Answer
Solution: $(-1,3,2)$
Work Step by Step
$x+y = 2$ Equation $(1)$
$-3y +z = -7$ Equation $(2)$
$2x+y-z = -1$ Equation $(3)$
Adding Equation $(2)$ and Equation $(3)$
$2x-3y+y+z-z = -8$
$2x-2y = -8$
Divide both sides by $2$
$x-y = -4$ Equation $(4)$
Adding Equation $(1)$ and Equation $(4)$
$x+x+y-y = 2-4$
$2x = -2$
$x= -1$
Substituting $x$ value in Equation $(1)$
$x+y = 2$
$-1+y = 2$
$y = 3$
Substituting $y$ value in Equation $(2)$
$-3y +z = -7$
$-3(3)+z = -7$
$-9 +z = -7$
$z = -7 +9$
$z = 2$
$x= -1$
$y = 3$
$z = 2$
Solution: $(-1,3,2)$
