Answer
The solution is $(-2,4,1)$
Work Step by Step
Use elimination for the first two equations:
$x - y + 2z = -4$
$3x + y - 4z=-6$
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$4x-2z=-10$ (1)
Add $-3$ times equation 2 to equation 3:
$-9x -3y +12z =18$
$2x + 3y + z = 9$
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$-7x+13z=27$ (2)
Add 7 times equation (1) to $4$ times equation (2):
$28x-14z=-70$
$-28x+52z=108$
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$38z=38$
$z=1$
Solve for x: $4x-2(1)=-10$
$x=-2$
Solve for y: $-2-y+2(1)=-4$
$y=4$
The solution is $(-2,4,1)$.
