How do you know if a graph is consistent?
A system with exactly one solution is called a consistent system. To identify a system as consistent, inconsistent, or dependent, we can graph the two lines on the same graph and see if they intersect, are parallel, or are the same line.
What is the graph of consistent independent system?
Consistent Independent: A system of linear equations is consistent independent when it has exactly one solution. When this is the case, the graphs of the lines in the system cross at exactly one point.
What is the graph of consistent and dependent equations?
If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
What is consistent dependent and inconsistent?
If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .
Is an inconsistent system dependent or independent?
An independent system of equations has exactly one solution (x,y) . An inconsistent system has no solution, and a dependent system has an infinite number of solutions.
What are consistent inconsistent and dependent equations?
What is dependent equation?
If the systems of equations are dependent, it means that there are an infinite number of solutions. So in order to determine a single solution (out of the infinite possibilities), the value of x will depend on what you choose as the value of y. That is, x varies with y (and y varies with x).
What is the graph of consistent and dependent equation?
How do you find the inconsistent equation?
Why are the equations of a graphing system consistent?
The lines intersect at one point. So the two lines have only one point in common, there is only one solution to the system. Because the lines are not the same the equations are independent. Because there is just one solution, this system is consistent. The system is consistent and the equations are independent.
When is a graph said to be inconsistent?
If two lines do not intersect at all, then the lines are said to be inconsistent. Inconsistent equations have graphs that never intersect. In this scenario the two lines will be parallel to each other. If two distinct lines lie in the same plane and never intersect, then the two lines must be parallel.
When does a consistent system become a dependent system?
If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.
When is a linear equation dependent and consistent?
In such a case, the pair of linear equations is said to be dependent and consistent. As represented in the graph below, the pair of lines coincides and therefore, dependent and consistent. Algebraically, when = = , then the lines coincides and the pair of equations is dependent and consistent.