Answer
$(-4,5,-20)$
Work Step by Step
$x+2y=6$ Equation $(1)$
$7x+3y+z=-33$ Equation $(2)$
$x-z=16$ Equation $(3)$
Add Equation $(2)$ and Equation $(3)$
$7x+3y+z+x-z=-33+16$
Combine like terms.
$8x+3y = -17$ Equation $(4)$
Multiply Equation $(1)$ by $-8$ and add with Equation $(4)$
$-8(x+2y)+8x+3y=-8(6)-17$
$-8x-16y+8x+3y=-48-17$
$-13y=-65$
$13y=65$
$y=5$
Substitute $y=5$ in Equation $(1)$ to get $x$
$x+2y=6$
$x+2(5)=6$
$x+10=6$
$x=6-10$
$x=-4$
Substitute $x$ value in Equation $(3)$ to get $z$
$x-z=16$
$-4-z=16$
$-z=16+4$
$-z=20$
$z= -20$
Solution: $(-4,5,-20)$
