Cramer's rule is well explained here:
http://www.purplemath.com/modules/cramers.htm
You will need to calculate the determinants of four 3x3 matrices. I assume you know how to do that. If not, it's high time to learn how.
Use crammers rule to solve the system of linear equations
3x+2y-z = 0
2x-y+z = 1
x-y+2y= -1
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