Solve[{x[1]+3x[2]-2x[3]+4x[5]==5,-x[3]+2x[4]+3x[6]==1,
2x[5]+x[6]==2},Table[x[i],{i,6}]]

     {{x[1] -> -1 - 3 x[2] + 4 x[4] + 8 x[6], 
      
                                                  x[6]
        x[3] -> -1 + 2 x[4] + 3 x[6], x[5] -> 1 - ----}}
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