Some systems of logical equations are inconvenient to solve in the form in which they are given. To simplify the system, you can recombine it.
In a system of logical equations, each equation must not be inconsistent when substituting variables. Hence, if each equation is true, the system can be represented as a conjunction of all equations. From this equation it is possible to compose a new system, more convenient for the display method.
If each equation is false, the system can be represented as a disjunction of all equations. Similarly, from this equation it is possible to compose a new system, more convenient for the display method.
Recombination is used to bring the system to the correct order of variables or to make the equations in the system of the same type.