Answer
The answer is $ x=0,y=0 $ and $ z=4$.
Work Step by Step
The given equations are
$ x+3y+5z=20 $ ... (1)
$ y-4z=-16 $ ... (2)
$ 3x-2y+9z=36 $ ... (3)
Multiply equation (1) by $-3$.
$ (-3)\cdot x+(-3)\cdot 3y+(-3)\cdot 5z=(-3)\cdot 20 $
Simplify.
$ -3x-9y-15z=-60 $ ... (4)
Add equation (3) and (4).
$ 3x-2y+9z-3x-9y-15z=36-60 $
Simplify.
$ -11y-6z=-24 $ ... (5)
Multiply equation (2) by $ 11 $.
$ 11\cdot y-11\cdot 4z= -11\cdot16 $
Simplify.
$ 11y-44z=-176 $ ... (6)
Add equation (5) and (6).
$ -11y-6z+11y-44z=-24-176 $
Simplify.
$ -50z=-200 $
Divide both sides by $-50$.
$\frac{-50z}{-50}=\frac{-200}{-50}$
Simplify.
$ z=4 $
Substitute $ z=4 $ into the equation (2).
$ y-4(4)=16 $
Simplify.
$ y-16=16 $
$ y=0 $
Substitute the values of $z $ and $y $ into the equation (1).
$ x+3(0)+5(4)=20 $
$ x+0+20=20 $
$ x=0 $.
