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In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x.
In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.
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How many solutions will a system have if the graph of the solution is not parallel lines?
infinitely many solutions :)
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
Can linear system that has more unknowns than equation be consistent?
yes it can . the system may have infinitely many solutions.
Explain how to identify whether an equation has no solution or infinitely many solutions?
An equation can be determine to have no solution or infinitely many solutions by using the square rule.
When you use the substitution method how can you tell that a has an infinite number of solutions?
If the process of substituting leads to an identity rather than an equation then the system has infinitely many solutions.
