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
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.
It is a system of linear equations which does not have a solution.
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.
if a dependent system of equation is solved, how many solutions will there be?
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.
One equation is simply a multiple of the other. Equivalently, the equations are linearly dependent; or the matrix of coefficients is singular.
When its matrix is non-singular.
This is a linear algebra question and it is incomplete since there are no equation which have to be solved.
By elimination and substitution
linear system is like a chemistry equation or math equation where on both sides it must balance. Nonlinear is a math equation or physics that does not appear to have a direct answer just like chaos theory. lulu254ever
An independent system of linear equations is a set of vectors in Rm, where any other vector in Rm can be written as a linear combination of all of the vectors in the set. The vector equation and the matrix equation can only have the trivial solution (x=0).
No, if two lines are parallel they will not have a solution.
A linear equation in n variables, x1, x2, ..., xn is an equation of the forma1x1 + a2x2 + ... + anxn = y where the ai are constants.A system of linear equations is a set of m linear equations in n unknown variables. There need not be any relationship between m and n. The system may have none, one or many solutions.
A linear equation in n-dimensional space is of the form a1x1 + a2x2 + ... + anxn + c = 0 where the ai are numerical constants and the xi are variables. The equation represents a straight line in n-dimensional space. A non-linear equation is one in which one or more of the xi have a power other than 1. The equation will represent a curve. A linear system is one in which you will get the same result if you change an input by the same amount - from whatever starting level. Otherwise the system is non-linear.
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its an equation that you can graph and when the points are connected, it makes a line. usually includes variables x and y.
Ordered Pair * * * * * An ordered SET. There can be only one, or even an infinite number of variables in a linear system.
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.
yes it can . the system may have infinitely many solutions.
one, zero, infinitely many.
Any solution to a system of linear equations must satisfy all te equations in that system. Otherwise it is a solution to AN equation but not to the system of equations.
The main advantage is that many situations cannot be adequately modelled by a system of linear equations. The disadvantage is that the system can often get very difficult to solve.
A "system of equations" implies that there is more than one equation.
That depends on what type of equation it is because it could be quadratic, simultaneous, linear, straight line or even differential
The statement "A system of linear equations is a set of two or more equations with the same variables and the graph of each equation is a line" is true.
A system of linear equations that has one unknown is a set of equations that all depend on the same variable. An example is y = 1 + 3x and y = 4 + 7x.