I think the traditional approach of implementing/solving linear equations is to convert them into matrix form and then repeatedly applying Gaussian Elimination until you solve the system or determine that it has no solution.

The easiest way of doing so is to either link to a solver library (maybe PDL has an equation system solver).

In reply to Re: How would you solve a user-inputted simple one-variable Linear Equation by Corion
in thread How would you solve a user-inputted simple one-variable Linear Equation by nat47

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