I was wondering if anyone would be able to provide help with a logical method of finding a redundant equation in a system of linear simultaneous equations. By 'redundant', I mean that I want to be able to find an equation which could be removed without preventing solutions from being found to the system of equations.
For example, if the system states that '$a=1$ and $b=2$' then neither equation is redundant because information is lost by removing either equation. However, if the system states that '$a=b-1, a=1,$ and $b=2$' then any one (but not more than one) of these equations could be removed without any information being lost. Another example of a system with redundant equations would be if '$a=b, a=2, b=2, c=1,$ and $d=c$'. I could remove any one (but not more than one) of the first three without losing any information, but neither of the last two equations can be removed.
The reason that I want a way to find the redundant equations is because I am making a program that will convert chemical equations into a system of simultaneous equations, then will solve the simultaneous equations and use the solutions to balance the original chemical equation. The function that I have made that solves the simultaneous equations does not work if there are any redundant equations, which is why I need a logical method for how to find any redundant equations, as I will make the computer remove a redundant equation before solving. The user cannot just change the way that they type in the chemical equation, because that would defy the laws of chemistry.
Thank-you in advance.