Mathematics for GIS Professionals

Equations With More Than One Unknown

What we’ll be doing here is solving equations that have more than one variable in them.  The process that we’ll be going through here is very similar to solving linear equations, which is one of the reasons why this is being introduced at this point.  There is however one exception to that.  Sometimes, as we will see, the ordering of the process will be different for some problems.  Here is the process in the standard order.


  1. Multiply both sides by the LCD to clear out any fractions.
  2. Simplify both sides as much as possible.  This will often mean clearing out parenthesis and the like.
  3. Move all terms containing the variable we’re solving for to one side and all terms that don’t contain the variable to the opposite side.
  4. Get a single instance of the variable we’re solving for in the equation.  For the types of problems that we’ll be looking at here this will almost always be accomplished by simply factoring the variable out of each of the terms.
  5. Divide by the coefficient of the variable.  This step will make sense as we work problems.  Note as well that in these problems the “coefficient” will probably contain things other than numbers.


It is usually easiest to see just what we’re going to be working with and just how they work with an example.

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