What makes a system consistent? Inconsistent?
Consistent if there is at least 1 solution (there can be infinite) Inconsistent if there is no solution
A system of equations is considered consistent when it has at least one solution that satisfies all the given equations in the system. In other words, the solution makes all the equations true at the same time.
On the other hand, a system of equations is considered inconsistent when it has no solution that satisfies all the given equations in the system. In other words, there is no possible value or set of values that makes all the equations in the system true at the same time.
For example, consider the following system of linear equations:
* 2x + 3y = 9
* 4x + 6y = 12
By using elimination or substitution, we can easily see that the second equation is a multiple of the first equation. Thus, this system has infinitely many solutions. Therefore, this system is consistent.
Now, consider the following system of linear equations:
* 2x + 3y = 9
* 4x + 6y = 15
By using either elimination or substitution, we can see that there is no value of x and y that can satisfy both equations at the same time. Thus, this system has no solution, which means it is inconsistent.
More Answers:
Mathematical Equivalence Of Linear Systems: How Row Equivalence Between Augmented Matrices Ensures Same SolutionsRow Equivalence In Linear Equations: Elementary Row Operations Explained
Matrix Size: Explaining M*N Notation For Rows And Columns