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What is an inconsistent system of equations?
How do you know if a system of linear equations is inconsistent?
Is a system of equations consistent or indeterminate?
What happens if a system is inconsistent?
How do you know if a system is consistent or inconsistent?
What is the difference between inconsistent and consistent?
In mathematics and particularly in algebra, a system of equations (either linear or nonlinear) 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.
Let both the lines to be parallel to each other, then there exists no solution because the lines never intersect. Algebraically, for such a case, a 1 /a 2 = b 1 /b 2 ≠ c 1 /c 2, and the pair of linear equations in two variables is said to be inconsistent.
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. Created by Sal Khan and Monterey Institute for Technology and Education. Questions.
- 5 min
- Sal Khan,Monterey Institute for Technology and Education
- "Inconsistent" is because it is not possible for both equations to hold simultaneously. They contradict each other in the sense that if one holds,...
- Yes, if the system includes other degrees (exponents) of the variables, but if you are talking about a system of linear equations, the lines can ei...
- Hi Isaiah, When you say "overlapped" do you mean the lines crossing? That's essentially the definition of a consistent system - that there is a sol...
- 2:10 As Sal said in the video, you can do it. He just wanted to make it clearer to view.
- To solve a system with three variable you need three equations. Combine them in two sets of two to get rid of one variable. Then combine these two...
- It's not right to say "a consistent line." You need more than 1 line to have *either* a "consistent" or "inconsistent" system. Then you can say tha...
- That is not a system of equations, so a single equation cannot be inconsistent, it is just a linear equation. If you had 2x - 2y = 14 as a second e...
- Yes these are based in planar geometry. So imagine a square room with 4 walls, a floor, and a ceiling. You see all sorts of lines that could be par...
- Yes. Good question. Sal explains that a solution is not needed (~ 5:00) since we're only asked whether the system is consistent or inconsistent. I...
Inconsistent systems arise when the lines or planes formed from the systems of equations don’t meet at any point and are not parallel (all of them or only two and the third meets one of the planes at some point.)
Sep 17, 2022 · Definition: Consistent and Inconsistent Linear Systems. A system of linear equations is consistent if it has a solution (perhaps more than one). A linear system is inconsistent if it does not have a solution.
Nov 21, 2023 · Learn about inconsistent systems of equations. Study graphs of inconsistent solutions, and discover how to identify inconsistent systems with examples. Updated: 11/21/2023.
A system of equations is said to be consistent if it has a solution, otherwise it is said to be an inconsistent. If a system of equations has more than one solution then it is said to be indeterminate .
