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What is a method used to solve systems of equations in which the solution is the point where the lines intersect?
Wiki User
∙ 15y ago
there are three methods: combination, substitution and decomposition.
Wiki User
∙ 15y ago
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What is the situation when two linear inequalities have no common solution?
To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
Which method of solving quadratic equations should be used when only an estimated solution is necessary?
Graphing
Why is substitution the best method in solving systems of equations?
It is not always the best method, sometimes elimination is the way you should solve systems. It is best to use substitution when you havea variable isolated on one side
Compare the symbolic method for solving linear equations to the methods of using a table or graph?
Equations = the method
What is the situation when two linear inequalities have no common solution?
To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent). To solve a system means to find the x- and y-values for which both of the equations are true. Systems of linear equations can be solved using a variety of methods. One method is to graph the equations as two lines and examine them. If the lines intersect at exactly one point, there is one solution to the system, and the system is called consistent. If the two lines are on top of one another, there are an infinite number of solutions, because each point on the line is considered a solution (this system is called dependent). If the two lines are parallel, there is no solution (this system is called inconsistent).
What has the author G R Lindfield written?
G. R. Lindfield has written: 'Modifications of the continuation method for the solution of systems of nonlinear equations'
What has the author Jeffrey S Scroggs written?
Jeffrey S. Scroggs has written: 'An iterative method for systems of nonlinear hyperbolic equations' -- subject(s): Algorithms, Hyperbolic Differential equations, Iterative solution, Nonlinear equations, Parallel processing (Computers)
How would you know if a linear system has a solution?
One way is to look at the graphs of these equations. If they intersect, the point of intersection (x, y) is the only solution of the system. In this case we say that the system is consistent. If their graphs do not intersect, then the system has no solution. In this case we say that the system is inconsistent. If the graph of the equations is the same line, the system has infinitely simultaneous solutions. We can use several methods in order to solve the system algebraically. In the case where the equations of the system are dependent (the coefficients of the same variable are multiple of each other), the system has infinite number of solutions solution. For example, 2x + 3y = 6 4y + 6y = 12 These equations are dependent. Since they represent the same line, all points that satisfy either of the equations are solutions of the system. Try to solve this system of equations, 2x + 3y = 6 4x + 6y = 7 If you use addition or subtraction method, and you obtain a peculiar result such that 0 = 5, actually you have shown that the system has no solution (there is no point that satisfying both equations). When you use the substitution method and you obtain a result such that 5 = 5, this result indicates no solution for the system.
How do you find the solution set of pair linear equations?
By the substitution method By the elimination method By plotting them on a graph
What is graphing method?
In systems of equations, the graphing method is solving x and y by graphing out the two equations. x and y being the coordinates of the two line's intersection.
What are the benefits and shortcomings of each method of systems of equations?
The answer will depend on what the "each method" refer to. The question provides no clue.
Which method of solving quadratic equations should be used when only an estimated solution is necessary?
Graphing
How can systems of equations be solved?
It depends on your level of expertise. The simplest method is to invert the matrix of coefficients.
What led up to Cramer's rule?
I suppose Cramer was looking for a generalized method to solve linear systems of equations. Using determinant's was his solution. I've posted a link to a neat site about Cramer's rule.
What is an Homotopy continuation Method?
A way to solve a system of equations by keeping track of the solutions of other systems of equations. See link for a more in depth answer.
What has the author Henry A Nogrady written?
Henry A. Nogrady has written: 'A new method for the solution of cubic equations'
