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What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
Are system of equations and system of linear equation the same?
No....not necessary
If a system has many solutions what kind of system of equations is it?
Coincidental equations are really the same and are the same line. They have infinite solutions meaning that any solution for one will be a solution for the other.
Is The graph of a system of equations with the same slope will have no solutions?
Yes.
Solve linear equations with complex coefficients on both sides?
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.
What are two or more linear equations using the same variables called?
A system of linear equations.
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.
What does a graph with infinitely many solutions look like?
they have same slop.then two linear equations have infinite solutions
Why Two dependent simultaneous linear equations have infinite solutions?
Two dependent linear equations are effectively the same equation - with their coefficients scaled up or down.
What is equations that have the same solutions?
Simultaneous equations have the same solutions.
What are the three types of possible solutions to a system of equations?
If the equations are linear, they may have no common solutions, one common solutions, or infinitely many solutions. Graphically, in the simplest case you have two straight lines; these can be parallel, intersect in a same point, or actually be the same line. If the equations are non-linear, they may have any amount of solutions. For example, two different intersecting ellipses may intersect in up to four points.
What does it mean if there are an infinite number of solutions for a system of linear equations?
It means that the equations are actually both the same one. When they're graphed, they both turn out to be the same line.
What is the definition of Simultaneous Linear Equations?
A system of linear equations is two or more simultaneous linear equations. In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
Does every pair of linear simultaneous equations have a solution?
Actually not. Two linear equations have either one solution, no solution, or many solutions, all depends on the slope of the equations and their intercepts. If the two lines have different slopes, then there will be only one solution. If they have the same slope and the same intercept, then these two lines are dependent and there will be many solutions (infinite solutions). When the lines have the same slope but they have different intercept, then there will be no point of intersection and hence, they do not have a solution.
What are equations that have the same answer?
Simultaneous equations have the same solutions
What are the possible solutions for a system of equations?
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
What is an equation that have the same solutions?
Simultaneous equations have the same solutions.
