posted by algebra on .
Explain how you can determine from the graph of a system of two linear equations in two variables whether it is an inconsistent system of equations.
3 possible cases:
1. one unique solution
the two graphs intersect at a single point, which also means that the slopes of the two lines are different.
2. no solution
The two lines are parallel and distinct, so there is no intersection in the Euclidean plane.
3. Infinite number of solutions
The two lines are parallel and coincident. Thus any point on the line(s) is a solution to the system of two equations.