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AutumnA system of linear equations is considered consistent if it has at least one solution that satisfies all the equations in the system.
Here’s a breakdown of the different possibilities:
Consistent System: This is the case where there’s at least one set of values for the variables that makes all the equations in the system true. There could be infinitely many solutions (all points on a line) or just one specific solution point.
Inconsistent System: This occurs when there are no solutions that satisfy all the equations simultaneously. The lines might be parallel or intersecting at a non-existent point.
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A system of linear equations is considered consistent if it has at least one solution that satisfies all the equations in the system.
Here’s a breakdown of the different possibilities:
Consistent System: This is the case where there’s at least one set of values for the variables that makes all the equations in the system true. There could be infinitely many solutions (all points on a line) or just one specific solution point.
Inconsistent System: This occurs when there are no solutions that satisfy all the equations simultaneously. The lines might be parallel or intersecting at a non-existent point.
For example, consider two equations:
This system is consistent because the solution (x = 0, y = 5) makes both equations true.
On the other hand, a system like: