Consistent System
A system is this if it has at least one solution
A consistent system is a set of equations in which each equation has a solution that satisfies each of the equations in the set. In simpler terms, a consistent system has at least one solution that satisfies all of the equations in the system.
For example, consider the following system of equations:
x + y = 4
2x – y = 1
This system is consistent because there is a solution that satisfies both of the equations. In this case, the solution is x = 1 and y = 3, which satisfies both equations simultaneously.
On the other hand, consider the following system of equations:
x + y = 4
2x + 2y = 8
This system is inconsistent because there is no solution that satisfies both of the equations. If we try to solve for x and y using the two equations, we end up with contradictory values. For instance, if we multiply the first equation by 2, we get 2x + 2y = 8. This is the exact same equation as the second equation, which means we can’t solve for x and y because there are many answers that could satisfy this.
In summary, a consistent system is one in which all of the equations have at least one solution, while an inconsistent system has no solutions. It’s crucial to determine whether a system is consistent or not as this can help you determine the kind of calculations you require to solve the equations.
More Answers:
Understanding the Concept of Unique Solutions in Mathematics, Engineering, and ProgrammingUnderstanding Linear Systems: Unique, Inconsistent, and Infinitely Many Solutions
Understanding Inconsistent Systems: Linear Equations with No Solution