Answer
Solution: $(1,-3,0)$
Work Step by Step
$y+ 2z = -3$ Equation $(1)$
$x-2y = 7$ Equation $(2)$
$2x-y+z = 5$ Equation $(3)$
Adding Equation $(1)$ and Equation $(2)$
$x+y-2y+2z=-3+7$
$x-y+2z = 4$ Equation $(4)$
Adding Equation $(2)$ and Equation $(3)$
$x+2x -2y -y +z = 7+5$
$3x-3y+z = 12$ Equation $(5)$
Multiplying Equation $(4)$ by $-3$
$-3x+3y-6z=-12$ Equation $(6)$
Adding Equation $(5)$ and Equation $(6)$
$3x-3x-3y+3y+z-6z = 12-12$
$-5z = 0$
$z= 0$
Substituting $z$ value in Equation $(1)$
$y+2(0)= -3$
$y = -3$
Substituting $y$ value in Equation $(2)$
$x-2(-3) = 7$
$x+6 = 7$
$x = 7 - 6$
$x = 1$
Solution: $(1,-3,0)$
