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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.
What else can I help you with?
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.
How many solutions did this linear system have?
To determine how many solutions a linear system has, we need to analyze the equations involved. A linear system can have one unique solution, infinitely many solutions, or no solution at all. This is usually assessed by examining the coefficients and constants of the equations, as well as using methods like substitution, elimination, or matrix analysis. If the equations are consistent and independent, there is one solution; if they are consistent and dependent, there are infinitely many solutions; and if they are inconsistent, there are no solutions.
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.
How many solutions will a system have if the graph of the solution is not parallel lines?
infinitely many solutions :)
How many solutions does a nonlinear system of equations?
None, one or many - including infinitely many.
How many solutions can a system of linear equations with two variables?
None, one or infinitely many.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
How many solutions did this linear system have?
To determine how many solutions a linear system has, we need to analyze the equations involved. A linear system can have one unique solution, infinitely many solutions, or no solution at all. This is usually assessed by examining the coefficients and constants of the equations, as well as using methods like substitution, elimination, or matrix analysis. If the equations are consistent and independent, there is one solution; if they are consistent and dependent, there are infinitely many solutions; and if they are inconsistent, there are no solutions.
What 3D shapes has a one square base?
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.
Can linear system that has more unknowns than equation be consistent?
yes it can . the system may have infinitely many solutions.
What are the three types of system of linear equations?
The three types arethe system has a unique solutionthe system has no solutionsthe system has infinitely many solutions.
How many solutions are there to the equation below?
Infinitely many
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.
How many solutions does this system have?
To determine how many solutions a system has, we need to analyze the equations involved. Typically, a system of linear equations can have one solution (intersecting lines), infinitely many solutions (coincident lines), or no solution (parallel lines). If you provide the specific equations, I can give a more accurate assessment of the number of solutions.
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.
