inconsistant system

Question

In your own words, what does it mean for a system to be consistent or inconsistent? Type an equation for g(x) that results, with f(x), in an inconsistent system:

f(x) = 2x - 8
g(x) = ?

How else can you describe the two lines in this inconsistent system?

Answer 1

Inconsistency occurs in two linear equations when no unique solution satisfying them both can be found. Inconsistency also occurs if three or more linear equations do not intersect at the same point when graphed.

In the case of linear equations there would be no solution if two lines were parallel. To be parallel they would have the same slope. If g(x) has the same slope as f(x) then it would have the form g(x)=2x+a, where a is a number, which may be zero. So g(x)=2x is an example. If a=-8, then f(x)=g(x), which is effectively one equation. A line cannot intersect itself.