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If a system of equations is dependentthat means all of the points on the graph of one equation match all of the other equation what types of lines would be the result of dependent system of equation?
In a dependent system of equations, the lines represented by the equations are identical; they overlap completely. This means that every point on one line is also a point on the other line. As a result, the lines appear as a single line on the graph, indicating infinitely many solutions.
What kind of lines are consistent dependent systems?
Consistent dependent systems are characterized by lines that overlap, meaning they represent the same line in a graph. This occurs when the equations of the lines are equivalent, resulting in an infinite number of solutions. In such cases, every point on the line is a solution to the system of equations, indicating that the lines are not only consistent but also dependent.
What is consistent system with independent equations?
A consistent system with independent equations is one in which there is at least one solution, and the equations do not overlap in their constraints, meaning that no equation can be derived from another. In such a system, the equations represent different planes (or lines in two dimensions), and they intersect at one unique point (in the case of two variables) or along a line (for three variables). This unique intersection indicates that the system has a single solution that satisfies all equations simultaneously.
When system of linear equations is graphed how is the graph of each equation related to the solutions of that equation?
When a system of linear equations is graphed, each equation is represented by a straight line on the coordinate plane. The solutions to each equation correspond to all the points on that line. The intersection points of the lines represent the solutions to the entire system; if the lines intersect at a point, that point is the unique solution. If the lines are parallel, there are no solutions, and if they overlap, there are infinitely many solutions.
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.
When graphing a system of equations with infinitely many solutions the Y intercept of the two lines will be?
When graphing a system of equations with infinitely many solutions, the two lines will be identical, meaning they overlap completely. As a result, they will share the same Y-intercept, which will be the point where both lines intersect the Y-axis. Therefore, the Y-intercept will be the same for both equations. This indicates that every point on the line is a solution to the system.
What are lines that have equivalent linear equations and overlap at every point when graphed?
coincidental -Lines that share the same solution sets.
What kind of lines are consistent dependent systems?
Consistent dependent systems are characterized by lines that overlap, meaning they represent the same line in a graph. This occurs when the equations of the lines are equivalent, resulting in an infinite number of solutions. In such cases, every point on the line is a solution to the system of equations, indicating that the lines are not only consistent but also dependent.
What is consistent system with independent equations?
A consistent system with independent equations is one in which there is at least one solution, and the equations do not overlap in their constraints, meaning that no equation can be derived from another. In such a system, the equations represent different planes (or lines in two dimensions), and they intersect at one unique point (in the case of two variables) or along a line (for three variables). This unique intersection indicates that the system has a single solution that satisfies all equations simultaneously.
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.
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.
Two lines intersect how many solutions does the system of equations have?
When two lines intersect, the system of equations has exactly one solution. This solution corresponds to the point of intersection, where both equations are satisfied simultaneously. If the lines are parallel, there would be no solutions, and if they coincide, there would be infinitely many solutions.
When solving a system of equations by graphing you will need to graph the equations on the same?
When solving a system of equations by graphing, you will need to graph the equations on the same coordinate plane. This allows you to visually identify the point where the two lines intersect, which represents the solution to the system. If the lines intersect at a single point, that point is the unique solution; if the lines are parallel, there is no solution; and if they coincide, there are infinitely many solutions.
