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Then they are simultaneous equations.

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Q: When lines overlap in a system of equations?
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What are lines that have equivalent linear equations and overlap at every point when graphed?

coincidental -Lines that share the same solution sets.


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 is true about the lines represented by this system of linear equations?

That they, along with the equations, are invisible!


A system of equations with exactly one solution?

A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.


What is true about a system of two linear equations that has no solution?

The two equations represent parallel lines.


Why do people call it a system when two lines intersect?

They do not. A set of lines can also be considered as a system of linear equations. But the fact that there is such a system does not mean that the lines intersect.


What types of lines would be the result of an inconsistent system of equation?

If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.


How many solutions is it possible for a system of linear equations to have?

one solution; the lines that represent the equations intersect an infinite number of solution; the lines coincide, or no solution; the lines are parallel


How many solutions will a system of equations have if the graphs of the lines intersect?

A system of equations will have one solution if the graphs of the lines intersect. This is because the lines intersect at a single point. Let's say that point is (a, b). The x = a, y = b is the one and only solution for the system.


A system of equations of two or more parallel lines is called a what?

Inconsistent


What is the point at which the lines intersect in a system of linear equations?

The coordinates of the point of intersection represents the solution to the linear equations.


What is a solution to a system of equations graphically?

Graphically, it is the point of intersection where the lines (in a linear system) intersect. If you have 2 equations and two unknowns, then you have a 2 lines in a plane. The (x,y) coordinates of the point where the 2 lines intersect represent the values which satisfies both equations. If there are 3 equations and 3 unknowns, then you have lines in 3 dimensional space. If all 3 lines intersect at a point then there is a solution to the system. With more than 3 variables, it is difficult to visualize more dimensions, though.