Answer
$x=1$
$y=5$
$z=6$
Work Step by Step
Using elimination for the first two equations:
$3x + y + z = 14$
$-x + 2y - 3z =-9$
Multiply both sides of the first equation by $-2$:
$-6x -2 y -2 z = -28$
$-x + 2y - 3z =-9$
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$-7x-5z=-37$ (1)
Then continue to use elimination for the first and third equations:
$3x + y + z = 14$
$5x-y+5z=30$
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$8x+6z=44$ (2)
From (1) and (2):
$-7x-5z=-37$
$8x+6z=44$
Multiply both sides of the first equation by $8$ and the second equation by $7$:
$-56x-40z=-296$
$56x+42z=308$
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$2z=12$
$z=6$
Solve for x: $8x+6(6)=44$
$8x=8$
$x=1$
Solve for y: $3(1) + y + 6 = 14$
$y=5$
