Answer
$(-1,2,0)$
Work Step by Step
Given Equations
$5x+7y=9$ Equation $(1)$
$14y-z=28$ Equation $(2)$
$4x+2z=-4$ Equation $(3)$
From Equation $(2)$
$14y-z=28$
$14y-28=z$
$z=14y-28$
Substituting $z=14y-28$ in Equation $(3)$
$4x+2z=-4$
$4x+2(14y-28)=-4$
$4x+28y-56=-4$
$4x+28y=-4+56$
$4x+28y=52$
$4(x+7y)=52$
$x+7y=13$ Equation $(4)$
Subtracting Equation $(4)$ From Equation $(1)$
$5x+7y-(x+7y)=9-13$
$5x+7y-x-7y=-4$
$4x=-4$
$x=-1$
Substituting $x$ value in Equation $(1)$
$5x+7y=9$
$5(-1)+7y=9$
$-5+7y=9$
$7y=9+5$
$7y=14$
$y=2$
Substituting $x$ value in Equation $(3)$
$4x+2z=-4$
$4(-1)+2z=-4$
$-4+2z=-4$
$2z=-4+4$
$2z=0$
$z=0$
Solution: $(-1,2,0)$
