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I think the first equation would be x+y+z=6. But, what will be the other two equations?

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x + 4*z = 2*y
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To me it seems like you only have two equations (the one you mentioned, and the one in the other comment) so in this case cramer's rule can't be used, since that is about systems of equations where the number of equations is equal to the number of variables.

I don't know what the question wants you to do, maybe you can give an answer that relates the values.
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3z = x + z = 2y

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