Answer
Infinitely many solutions.
Work Step by Step
Using elimination for the first two equations:
$x + 5y - 2z = -1$
$-x - 2y +z = 6 $
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$3y-z=5$ (1)
Then continue to use elimination for the first and the third equations:
$x + 5y - 2z = -1$
$-2x - 7y + 3z = 7 $
Multiply both sides of the first equation by $2$:
$2x + 10y - 4z = -2$
$-2x - 7y + 3z = 7 $
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$3y-z=5$(2)
Using elimination for equation (1) and (2):
$3y-z=5$
$3y-z=5$
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$0=0$
The system has infinitely many solutions.
