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It means that at least one of the equations can be expressed as a linear combination of some of the other equations.
A linear combination of equations is the addition (or subtraction) of equations. And since an equation can be added several times, it includes multiples of equations.
For example, if you have
x + 2y = 3
and
2x + y = 4
Then adding 2 times the first and 3 times the second gives
8x + 7y = 18
This is, therefore, dependent on the other 2.
If you have n unknown variables, there will be a unique solution if, and only if, you must have a set of n independent linear equations.
What else can I help you with?
Are system of equations and system of linear equation the same?
No....not necessary
If a dependent system of equations is solved how many solutions will there be?
if a dependent system of equation is solved, how many solutions will there be?
Why could a system of linear equations have two solutions?
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
Is there any system which involves one nonlinear equation and one linear equation?
Yes
When will the system of linear equation be consistent?
When its matrix is non-singular.
What is inconsistent system of linear equation?
It is a system of linear equations which does not have a solution.
What is consistent and dependent?
The terms consistent and dependent are two ways to describe a system of linear equations. A system of linear equations is dependent if you can algebraically derive one of the equations from one or more of the other equations. A system of linear equations is consistent if they have a common solution.An example of a dependent system of linear equations:2x + 4y = 84x + 8y = 16Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 16, which gives 16 = 16.No new information was gained from the second equation, because we already knew 16 = 16, so these two equations are dependent.An example of an inconsistent system of linear equations:Because consistency is boring.2x + 4y = 84x + 8y = 15Solve the first equation for x:x = 4 - 2yPlug that value of x into the second equation:16 - 8y + 8y = 15, which gives 16 = 15.This is a contradiction, because 16 doesn't equal 15. Therefore this system has no solution and is inconsistent.
Are system of equations and system of linear equation the same?
No....not necessary
A system of two linear equations has infinitely many solutions if?
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
If a dependent system of equations is solved how many solutions will there be?
if a dependent system of equation is solved, how many solutions will there be?
What is a dependent system?
A dependent system is defined as "a system of equations that has infinite solutions." It is an equation that is used in various mathematical situations.
Why could a system of linear equations have two solutions?
A system of linear equations cannot have two distinct solutions if it is consistent and defined in a Euclidean space. If two linear equations intersect at a single point, they have one solution; if they are parallel, they have no solutions. However, if the equations are dependent, meaning one equation is a multiple of the other, they represent the same line and thus have infinitely many solutions, not just two. Therefore, in standard scenarios, a system of linear equations can either have one solution, no solutions, or infinitely many solutions, but not exactly two.
Is there any system which involves one nonlinear equation and one linear equation?
Yes
What is a system of equations that has at least one solution?
a linear equation
When will the system of linear equation be consistent?
When its matrix is non-singular.
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
Which ordered pair is a solution of the linear system?
This is a linear algebra question and it is incomplete since there are no equation which have to be solved.
