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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.

Q: What kind of system has infinitely many solutions?

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infinitely many solutions :)

None, one or infinitely many.

yes it can . the system may have infinitely many solutions.

An equation can be determine to have no solution or infinitely many solutions by using the square rule.

If the process of substituting leads to an identity rather than an equation then the system has infinitely many solutions.

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infinitely many solutions :)

None, one or many - including infinitely many.

None, one or infinitely many.

A system of linear equations can only have: no solution, one solution, or infinitely many solutions.

yes it can . the system may have infinitely many solutions.

There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.There are infinitely many possible solutions. The question needs to be more specific.

The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.

Infinitely many

An equation can be determine to have no solution or infinitely many solutions by using the square rule.

If the process of substituting leads to an identity rather than an equation then the system has infinitely many solutions.

NO! A linear system can only have one solution (the lines intersect at one point), no solution (the lines are parallel), and infinitely many solutions (the lines are equivalent).

Infinitely many.