Which equation is consistent 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 .
What makes an equation inconsistent?
When a system of equations has no solution, it’s called inconsistent. If a system of equations is inconsistent, then when we try to solve it, we will end up with a statement that makes no sense, and if we observe the graphs of the equations involved, we’ll see that they never intersect.
Which system is inconsistent and 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.
Which equations are consistent?
In mathematics and particularly in algebra, a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.
What is consistent system of equations?
A consistent system of equations has at least one solution, and an inconsistent system has no solution.
What is the system of equations is called which have no solution?
MA, Stanford University. A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel. A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.
How do you tell if a system of equations has infinitely many?
Conditions for Infinite Solution The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
What is a consistent system of equations?
A consistent system of equations has at least one solution, and an inconsistent system has no solution. Watch an example of analyzing a system to see if it’s consistent or inconsistent.
Is parallel lines consistent?
If the two equations describe parallel lines, and thus lines that do not intersect, the system is independent and inconsistent. If the two equations describe the same line, and thus lines that intersect an infinite number of times, the system is dependent and consistent.