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What is a inconsistent line?
its a system of equations, with no solution
What is the solution of the system 2x plus 3y equals 2 and 4x plus 6y equals 4?
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
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.
What is a system of equations that has infinite solutions?
When the two equations actually represent the same line, the solution to the system will be all points on the line. For example take the line y=x+2, if we multiply both sides of the equation by 2 we do not change anything about the line. So the equation 2y=2x+4 is really the same equation. The solution to the system y=x+2 and 2y=2x+4 is all the points ( all the real numbers) on the line. We often write this {(x,y)|y=x+2}
If a system of linear equations has no solution then the graph of the two equationsmust be what kind of line?
parallel
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 is a inconsistent line?
its a system of equations, with no solution
On a graph the solution of a system of a linear equations will be represented by what?
The set of points the graphed equations have in common. This is usually a single point but the lines can be coincident in which case the solution is a line or they can be parallel in which case there are no solutions to represent.
What system of equations has no solution?
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
What type of system equation produces the solution set infinite solution?
If the equations of the system are dependent equations, which represent the same line; therefore, every point on the line of a dependent equation represents a solution. Since there are an infinite number of points on a line, there is an infinite number of simultaneous solutions. For example, 3x + 2y = 8 6x + 4y = 16
What is the solution to this system of equations y equals -3x-2?
-1
What is a system of linear equations?
A system of linear equations determines a line on the xy-plane. The solution to a linear set must satisfy all equations. The solution set is the intersection of x and y, and is either a line, a single point, or the empty set.
What is the solution of the system 2x plus 3y equals 2 and 4x plus 6y equals 4?
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
How do you interpret the solution of a system of equations by the corresponding graph?
The solution of a system of equations corresponds to the point where the graphs of the equations intersect. If the equations have one unique point of intersection, that point represents the solution of the system. If the graphs are parallel and do not intersect, the system has no solution. If the graphs overlap and coincide, the system has infinitely many solutions.
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.
What is a system of equations that has infinite solutions?
When the two equations actually represent the same line, the solution to the system will be all points on the line. For example take the line y=x+2, if we multiply both sides of the equation by 2 we do not change anything about the line. So the equation 2y=2x+4 is really the same equation. The solution to the system y=x+2 and 2y=2x+4 is all the points ( all the real numbers) on the line. We often write this {(x,y)|y=x+2}
How does graphing a linear system help you verify the results of solving a linear system algebraically?
You see the point the two lines cross, if they do. This is the solution to the system since it is the values of (x,y) that are on both lines The solution is a sytems is those points, if any, (x,y) that satisfy both equations. That is the same as saying they are on both lines. If you graph the equations, this is the same as saying the points that are in the intersection of the lines. This is why parallel lines represent a system with no solution and if two equations are the same line there is an infinite number of solutions.
