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Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
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 system of equations that has at least one solution is called?
A system of equations that has at least one solution is called a consistent system. This means that the equations in the system intersect at least at one point in their graphical representation. If there is exactly one solution, the system is termed independent, while if there are infinitely many solutions, it is called dependent.
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 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.
Describe a consistent independent system of linear equations?
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
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.
How many solutions does the nonlinear system of equations graphed below have?
2
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).
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.
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.
System of equations in slope-intercept form that has one solution Using complete sentences explain why this system has one solution?
Provide a system of equations in slope-intercept form that has one solution. Using complete sentences, explain why this system has one solution.
what system of equations that has at least one solution is called?
A system of equations that has at least one solution is called a consistent system. This means that the equations in the system intersect at least at one point in their graphical representation. If there is exactly one solution, the system is termed independent, while if there are infinitely many solutions, it is called dependent.
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 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 does the solution represent when a system of equations has a single solution?
The graphs of the two equations have only one intersection point.
A system of linear equations that has soluton is?
A system of linear equations that has at least one solution is called consistent.
