Answer
The fill in the blanks are
$ -2 $
$ -4 $.
Work Step by Step
The given equations are
$ x+y-z=-1 $ ... (1)
$ 2x-2y-5z=7 $ ... (2)
$ 4x+y-2z=7 $ ... (3)
Multiply the equation (1) by $ -2 $
$ (-2)\cdot x+(-2)\cdot y-(-2)\cdot z=-(-2)\cdot 1$
$ -2x-2y+2z=2 $ ... (4)
Now add equation (4) and equation (2).
$ -2x-2y+2z+2x-2y-5z=2+7 $
add like terms
$ -4y-3z=9 $
$x$ eliminated.
Multiply the equation (1) by $ -4 $
$ (-4)\cdot x+(-4)\cdot y-(-4)\cdot z=-(-4)\cdot 1$
$ -4x-4y+4z=4 $ ... (5)
Now add equation (5) and equation (3).
$ -4x-4y+4z+4x+y-2z=4+7 $
$ -3y+2z=11 $
$x$ eliminated.
