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# How many solutions might a system of equations have?

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## Related Questions

###### Asked in Math and Arithmetic, Algebra

### If a system of equations is independent how many soultions will it have?

A system of equations may have any amount of solutions. If the
equations are linear, the system will have either no solution, one
solution, or an infinite number of solutions. If the equations are
linear AND there are as many equations as variables, AND they are
independent, the system will have exactly one solution.

###### Asked in Cars & Vehicles, Algebra

### How many solutions does an inconsistent system of equations have?

If a system is inconsistent it cannot have any
solutions.
A system of equations is considered inconsistent when the lines
are parallel which means they never intersect so there are no
solutions.
A system is considered consistent when they intersect at one
point and have one solution (Also known as an independent system of
equations).
Dependent Systems are when the lines coincide (the same
equation) so they have an infinite number of solutions.

###### Asked in Algebra, Linear Algebra

### What is linear algebra used for?

Linear algebra is used to analyze systems of linear equations.
Oftentimes, these systems of linear equations are very large,
making up many, many equations and are many dimensions large. While
students should never have to expect with anything larger than 5
dimensions (R5 space), in real life, you might be dealing with
problems which have 20 dimensions to them (such as in economics,
where there are many variables).
Linear algebra answers many questions. Some of these questions
are:
How many free variables do I have in a system of equations?
What are the solutions to a system of equations?
If there are an infinite number of solutions, how many
dimensions do the solutions span?
What is the kernel space or null space of a system of equations
(under what conditions can a non-trivial solution to the system be
zero?)
Linear algebra is also immensely valuable when continuing into
more advanced math topics, as you reuse many of the basic
principals, such as subspaces, basis, eigenvalues and not to
mention a greatly increased ability to understand a system of
equations.

###### Asked in Algebra

### How do you know when an algebraic equation has infinitely many solutions?

A system of equations has an infinite set of solutions when the
equations define the same line, such that for ax + by = c, the
values for two equations is a1/a2 + b1/b2 = c1/c2.
Equations where a variable drops out completely, e.g.
3x - y = 6x -2y
there are either an infinite number of solutions, or no solution
at all.