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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 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.
Why a system of linear equations cannot have exactly two solutions?
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
Can a system of linear equations in two variables have infinitely solutions?
Yes.
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.
How many solutions does the nonlinear system of equations graphed below have?
2
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.
How many solutions does the nonlinear system of equations graphed when the graph open up and down?
A system of equations means that there are more than one equations. The answer depends on the exact function(s).
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 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 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.
If a system of equations is inconsitient how many solutions will it have?
If a system of equations is inconsistent, there are no solutions.
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
The graph is not visible and so it is not possible to tell whether the lines are in a space with 2 dimensions or more. In 2-d space there is one solution whereas in more dimensions there may be none or one.
The two lines graphed below are not parallel. How many solutions are there to the system of equations?
The graph is not visible and so it is not possible to tell whether the lines are in a space with 2 dimensions or more. In 2-d space there is one solution whereas in more dimensions there may be none or one.
Describe a system of equations that would be better graphed using graphing technology?
no.
Provide a system of TWO equations in slope-intercept form with no solutions how to explain why this system has no solutions?
y = mx + b y = mx + c c does not equal b the two equations are parallel and will therefore never intersect with one another.
How many solutions does the system of linear equations shown have?
As there is no system of equations shown, there are zero solutions.
