# Defining and Solving Systems of Equations Using Matrix Tables

I've defined a system of equations, but I been unable to get Mathematica to solve for the individual variables created by matrix tables.

Table[tair[j,i],{j,y},{i,x}]==c*Table[Sum[t[j,i],{j,j+1,y}]-Sum[tair[j, i],{j,j+1,y}],{j,y},{i,x}]

Table[tout[i],{i,x}]==c*Table[Sum[t[j,i],{j,1,y}]-Sum[tair[j,i],{j,1,y}],{i, x}]

tout[1]=16
tout[2]=16
tair[2,1]=0
tair[2,2]=0


C is a known constant. To confirm my math, I've used values of 2 for y and x and I've written out the 6 resulting equations in Mathematica, defining variables explicitly rather than through tables:

tair11,tair12,tair21,tair22,t11,t12,t21,t22,tout1,tout2


Using the Solve function, I get the right answer. But since I want to be able to increase the order of y and x to say, 100, a manual enumeration process is not practicable. My question: what must I do syntactically to get Mathematica to solve for these variables? Even a simple example not related to my code would be most helpful.

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Like this? Array[C, 5] /. First[Solve[Thread[HilbertMatrix[5].Array[C, 5] == Range[5]], Array[C, 5]]] –  Guess who it is. Apr 19 '13 at 18:02
This is intriguing, thanks. I'm not familiar with the thread command, let me do some homework there. –  Thermoguy Apr 19 '13 at 18:27
Thread doesn't seem to help me solve for the values :( –  Thermoguy Apr 19 '13 at 23:08
Finally figured out my problem, thanks –  Thermoguy Apr 19 '13 at 23:51