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How do i solve for 18 variables with 18 equations?

Hello,

maybe some of you can help me with this. 

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In the equations are variables F_[i][j] and GG_[i][j] (for i=1,2,3 and j=1,2,3). There are 5 Equations that equal 0 and 1 Equation that equals Q(given). 
Is there a better way to try and solve this equations? 

Thank you


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