Answer
No solution
Work Step by Step
Use elimination for the first and third equations:
$w + x + y + z = 2$
$-w + 2x -y + 2z =-2$
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$3x+3z=0$ (1)
Then continue to use elimination for the second and third equations:
$2w - x + 2y - z = 1$
$-w + 2x -y + 2z =-2$
Multiply both sides of the second equation by $2$:
$2w - x + 2y - z = 1$
$-2w + 4x -2y + 4z =-4$
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$3x+3z=-3$ (2)
From (1) and (2):
$3x+3z=0$
$3x+3z=-3$
Multiply both sides of the first equation by $-1$:
$-3x-3z=0$
$3x+3z=-3$
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$0x+0z=-3$
Hence, there is no solution for this system.
