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What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
What does it mean when a system of two linear equations does not have a solution?
When a system of two linear equations does not have a solution, it means that the lines represented by the equations are parallel and will never intersect. This occurs when the equations have the same slope but different y-intercepts. As a result, there is no set of values for the variables that can satisfy both equations simultaneously. In such cases, the system is considered inconsistent.
Is it possible to have a system of equations that has more than one solution?
Yes, a system of equations can have more than one solution if the equations represent the same line or plane in a geometric sense. In such cases, there are infinitely many solutions that satisfy all equations simultaneously. This typically occurs in systems of linear equations where the equations are dependent. Conversely, if the equations are independent, the system will either have a unique solution or no solution at all.
What does a single solution to a system of equations mean?
It represents the point of intersection on a graph.
What is a system of linear equations that has no solution?
there is no linear equations that has no solution every problem has a solution
If a system of equations is independent how many soultions will it have?
A system of equations may have any amount of solutions. If the equations are linear, the system will have either no solution, one solution, or an infinite number of solutions. If the equations are linear AND there are as many equations as variables, AND they are independent, the system will have exactly one solution.
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 the solution of a system of linear equations in two variables?
The solution of a system of linear equations is a pair of values that make both of the equations true.
What does it mean when a system of two linear equations does not have a solution?
When a system of two linear equations does not have a solution, it means that the lines represented by the equations are parallel and will never intersect. This occurs when the equations have the same slope but different y-intercepts. As a result, there is no set of values for the variables that can satisfy both equations simultaneously. In such cases, the system is considered inconsistent.
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.
Is it possible to have a system of equations that has more than one solution?
Yes, a system of equations can have more than one solution if the equations represent the same line or plane in a geometric sense. In such cases, there are infinitely many solutions that satisfy all equations simultaneously. This typically occurs in systems of linear equations where the equations are dependent. Conversely, if the equations are independent, the system will either have a unique solution or no solution at all.
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.
Is (1 10) a solution to this system of equations?
No because there are no equations there to choose from.
When solving a system of equations by graphing how is the solution found?
The solution is the coordinates of the point where the graphs of the equations intersect.
How do you know if a system has one solution?
If the equations or inequalities have the same slope, they have no solution or infinite solutions. If the equations/inequalities have different slopes, the system has only one solution.
