Answer
$(2,-1,0)$
Work Step by Step
$7x+4y=10$ Equation $(1)$
$x-4y+2z=6$ Equation $(2)$
$y-2z=-1$ Equation $(3)$
Equation $(1)$ + Equation $(2)$
$(7x+4y)+(x-4y+2z)=10+6$
$8x+2z=16$ Equation $(4)$
$4\times$Equation $(3)$ + Equation $(2)$
$4(y-2z)+(x-4y+2z)=4(-1)+6$
$(4y-8z)+(x-4y+2z)=-4+6$
$x-6z=2$ Equation $(5)$
$(3 \times$ Equation $(4))$ + $($Equation $(5))$
$3(8x+2z)+(x-6z)=3(16)+2$
$(24x+6z)+(x-6z)=50$
$25x=50$
$x=2$
Substitute $x=2$ into Equation $(5)$ to get $z$.
$2-6z=2$
$-6z=0$
$z=0$
Substitute $z=0$ into Equation $(3)$ to get $y$.
$y-2(0)=-1$
$y=-1$
$(2,-1,0)$ satisfies the given equations.
Solution is $(2,-1,0)$
