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Can systems of equations with the same slopes and different y-intercepts have no solution?
Wiki User
∙ 13y ago
It is a correct statement.
Wiki User
∙ 13y ago
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What is a systems of equations that has the same solution set as another system?
They are called equivalent systems.
What are the three types of systems of linear equations and their characteristics?
Independence:The equations of a linear system are independent if none of the equations can be derived algebraically from the others. When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.Consistency:The equations of a linear system are consistent if they possess a common solution, and inconsistent otherwise. When the equations are inconsistent, it is possible to derive a contradiction from the equations, such as the statement that 0 = 1.Homogeneous:If the linear equations in a given system have a value of zero for all of their constant terms, the system is homogeneous.If one or more of the system's constant terms aren't zero, then the system is nonhomogeneous.
What can systems of equations be solved by?
By elimination or substitution
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
When are systems of linear equations used?
In coordinated geometry on the Cartesian plane
When equations of linear systems have different slopes how many solutions does it have?
One solution
Which of the following systems of equations has no solution?
If they are quadratic equations then if their discriminant is less than zero then they have no solutions
What is a systems of equations that has the same solution set as another system?
They are called equivalent systems.
Systems of equations have one solution?
Systems of equations can have just about any number of solutions: zero, one, two, etc., or even infinitely many solutions.
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
Why are systems of equations important?
A single equation is several unknowns will rarely have a unique solution. A system of n equations in n unknown variables may have a unique solution.
Must solutions to systems of linear equalities satisfy both equalities?
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.
When solving systems of linear equations what does the solution represent?
A single point, at which the lines intercept.
Give 6 different uses of matrices.?
CryptographyComputer graphicsCombinatoricsData recoverySolving systems of linear equations for arbitrary outputted valuesSolving systems of differential equations.
When solving systems of linear equation's when would you get no solution as an answer?
You get no solution if the lines representing the graphs of both equations have the same slope, i.e. they're parallel. "No solution" is NOT an answer.
What is a method used to solve systems of equations in which the solution is the point where the lines intersect?
there are three methods: combination, substitution and decomposition.
What has the author Claude Pommerell written?
Claude Pommerell has written: 'Solution of large unsymmetric systems of linear equations' -- subject(s): Equations, Iterative methods (Mathematics), Numerical solutions
