Answer
The solution is
$x=1 $,
$ y=-5 $
and $z=-6 $
Work Step by Step
Given equations are
$ x+y=-4 $ ... (1)
$ y-z=1 $ ... (2)
$ 2x+y+3z=-21 $ ... (3)
Multiply equation (2) by $3 $.
$ 3\cdot y - 3\cdot z= 3\cdot 1 $
$ 3y-3z=3 $ ... (4)
Add equation (3) and (4).
$ 2x+y+3z+3y-3z=-21+3 $
$ 2x+4y=-18 $ ... (5)
Multiply equation (1) with $ -2$.
$ (-2)\cdot x+(-2)\cdot y = -(-2)\cdot 4 $
$ -2x-2y=8 $ ... (6)
add equation (5) and (6).
$ 2x+4y-2x-2y=-18+8 $
$ 2y=-10 $
$ y=-5 $ Substitute into equation (1)
$ x-5=-4 $
$ x=-4+5 $
$ x=1 $
Substitute the value of $y$ into equation (2).
$ -5-z=1 $
$z=-5-1 $
$ z=-6 $
