The rule to determine the number of solutions in a system of linear equations depends on the relationship between the number of equations and the number of unknowns.
The rule to determine the number of solutions a system of linear equations will have is based on the concept that the number of solutions is related to the number of linearly independent equations the system contains.
For example, a system with more equations than unknowns may not have solutions if the equations are dependent, while a system with an equal number of equations and unknowns typically has a unique solution, and a system with fewer equations than unknowns may have infinitely many solutions.
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