if the system of linear equations results in 2 parallel lines, what type of system is obtained? What if the result is 2 intersecting lines?

Question

if the system of linear equations results in 2 parallel lines, what type of system is obtained?  What if the result is 2 intersecting lines?

tkhunny · Answer

2 DISTINCT parallel lines - inconsistent

whpalmer4 · Answer

2 parallel lines means there are no solutions, because there are no points which fall on both lines.  Inconsistent is the technical name for this.

2 intersecting lines have one point in common, which is a solution to both equations.  Such a system is called consistent, unlike the case of the two parallel lines.

If you have 2 lines which are identical (coincident), the system has an infinite number of solutions, because every point on the line is a solution.