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There are three kinds:the equations have a unique solutionthe equations have no solutionthe equations have infinitely many solutions.
simultaneous equations
It is a set of equations, which is also called a system of equations. There may be no solution, a single (unique) solution or more than one - including infinitely many.
You don't need ANY factor. To find a unique solution, or a few, you would usually need to have as many equations as you have variables.