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If one (or more) of the equations can be expressed as a linear combination of the others.
This is equivalent to the statements
the matrix of coefficients does not have an inverse (or is singular),
or
the determinant of the matrix of coefficients is zero.
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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?
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
What is a solution to a system?
an ordered pair that makes both equations true
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.
Methods on system of linear equations?
Lety be the column vector the dependent variable,M be the matrix of coefficients, andx be the column vector of variablesso that the system of equations may be represented by y = Mx.Then the solution set is obtained by left-multiplying both sides by M^-1that is x = M^-1*y
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.
What are equations with the same solution?
Equations with the same solution are called dependent equations, which are equations that represent the same line; therefore every point on the line of a dependent equation represents a solution. Since there is an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 2x + y = 8 4x + 2y = 16 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. A system of linear equations is consistent if there is only one solution for the system. A system of linear equations is inconsistent if it does not have any solutions.
If a system of linear equations has many solutions what would be the correct mathematical description of the system?
dependent
What is system dependability?
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.
How many solutions does an consistent and dependent system of equations have?
It has more than one solutions.
What is an ordered pair that makes all equations in a system true?
That would be the "solution" to the set of equations.
If a system of equations is dependent how many solutions will it have?
Infinite simultaneous solutions. (The two equations represent the same line) OR If your in nova net the answer should be ( Many )
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.
What is a solution to a system?
an ordered pair that makes both equations true
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.
What makes an equation either inconsistent consistent dependent or independent?
That doesn't apply to "an" equation, but to a set of equations (2 or more). Two equations are:* Inconsistent, if they have no common solution (a set of values, for the variables, that satisfies ALL the equations in the set). * Consistent, if they do. * Dependent, if one equation can be derived from the others. In this case, this equation doesn't provide any extra information. As a simple example, one equation is the same as another equation, multiplying both sides by a constant. * Independent, if this is not the case.
