What does it mean when a system is consistent?

To sum up, a consistent system has at least one solution. An inconsistent system has NO solution at all. Now for the other pair. " Dependent" versus "Independent." When a system is "dependent," it means that ALL points that work in one of them ALSO work in the other one.
A.

How can you tell if a system is consistent or inconsistent?

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 an inconsistent equation?

    A system of equations which has no solutions. Note: Attempts to solve inconsistent systems typically result in impossible statements such as 0 = 3. See also. Consistent system of equations, overdetermined system of equations, underdetermined system of equations, linear system of equations.
  • What is the solution to the system?

    In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations.
  • How many solutions are in a parallel line?

    Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
B.

When a system of two linear equations is inconsistent?

Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution. The third graph above, "Case 3", appears to show only one line.
  • How many solutions does a system of linear equations have if it is consistent?

    A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent .
  • How can you find the solution of a system of linear equations by graphing?

    The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
  • What does it mean to be a solution to a system of equations?

    In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations.
C.

What is a dependent system of linear equations?

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 find the solution to a system of equations?

    There can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.
  • Which are methods used to solve linear systems?

    There are three ways to solve systems of linear equations in two variables:
    • graphing.
    • substitution method.
    • elimination method.
  • What does the intersection of the two graphs mean?

    Remember, the graph of a line represents every point that is a possible solution for the equation of that line. So when the graphs of two equations cross, the point of intersection lies on both lines, meaning that it is a possible solution for both equations.

Updated: 21st November 2019

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