Thanks for your answer, David. This is not a reaction balancing problem but the analysis of the compositional data of a compound to find out its chemical structure. The compound is a oligomer (aprox. DP = 246) on which we have attached a number of three different types of substituents, one of them being also another oligomer (aprox. DP = 45). We expected that the algebraic analysis of the data from elemental analysis (for C, H and N) and ICP-MS (for P, Cu, Li and Na) could give as an average number of each motif present on the final structure. However, we obtained some results with no physical sense (negative numbers, a number of anchoring points too large, etc). I'm not familiar with Grassmann algebra, so I cannot tell wether it may be able to manage this problem or not. What's your opinion? Thank you again for your time.

May be wrong here, but there are 6 equations and 5 unknowns, if you remove eqn 6 or 5 it solves to same results, if you also stipulate in findinstance, 2, i.e. at end of the line before last bracket put ,2 it only finds one solution, so there are no more possible solutions to find. Also if you want exact results replace all the decimal numbers with an equivalent fraction, so c1 would be 12011/1000 etc, the results are then

{n -> 173215706769233171913184126360/3881732658541918082745706259, 
 m -> 2011250091823242432811209994438/3881732658541918082745706259, 
 x -> 57903752528057699427340882944/3881732658541918082745706259, 
 y -> 132095/89712, 
 z -> 64378109342715479415997877210/3881732658541918082745706259}