There are three kinds:
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There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.
independent variable,depedent variable and control variable are the 3 kinds of variables.
the three kinds of variables are independent,dependent and controlled
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
Three different kinds: none, one and infinitely many.