Search results
- Generated by AI
Creating an answer for you using AI...
Loading... If a system of equations is inconsistent, then the equations cannot be true together leading to contradictory information, such as the false statements 2 = 1, or and (which implies 5 = 6).
People also ask
What is inconsistent system of equations?
How do you know if a system of linear equations is consistent?
What is a consistent system of equations?
Why is there no solution to a linear equation?
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.
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.
- Two Variable System of Equations with Infinitely Many Solutions
- Two Variable Systems of Equations with No Solution
- Three Variable Systems of Equations with Infinite Solutions
- Three Variable Systems with No Solution
The equations in a two variable system of equations are linear and hence can be thought of as equations of two lines. When these two lines are parallel, then the system has infinitely many solutions. When two lines are parallel, their equations can usually be expressed as multiples of each other and that’s usually a quick way to spot systems with i...
There also exist two variable system of equations with no solution at all. This happens when as we attempt to solve the system we end up an equation that makes no sense mathematically. For example, solve the system of equations below: Using matrix method we can solve the above as follows: Reducing the above to Row Echelon form can be done as follow...
When discussing the different methods of solving systems of equations, we only looked at examples of systems with one unique solution set. These are known as Consistent systems of equations but they are not the only ones. Three variable systems of equations with infinitely many solution sets are also called consistent. Since the equations in a thre...
Three variable systems of equations with no solution arise when the planed formed by the equations in the system neither meet at point nor are they parallel. As a result, when solving these systems, we end up with equations that make no mathematical sense. For example; solve the system of equations below Solution: Using Matrix method: In the last r...
Feb 24, 2012 · You can conclude the system has an infinite number of solutions. This is called a consistent-dependent system. inconsistent system: A system with no solutions is called an inconsistent system. For linear equations, this occurs with parallel lines. substitute: In algebra, to substitute means to replace a variable or term with a specific value.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y- intercepts. There are no points common to both lines; hence, there is no solution to the system.
Oct 31, 2012 · We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections...
- 9 min
- 151.4K
- Khan Academy
