In the world of math, where lines intersect,
Three types of systems we must detect.
Each with its own unique solution space,
Let’s explore them all with poetic grace.
First, the independent system stands tall,
One point of intersection, that’s all.
Two lines cross at a single spot,
A unique solution, tied in a knot.
Like two paths meeting at journey’s end,
One answer where the lines transcend.
Next, we find the dependent pair,
Identical lines, a matching affair.
Infinite solutions along their track,
Every point a match, none held back.
Like parallel mirrors, reflections galore,
Countless answers, forevermore.
Last, we meet the inconsistent crew,
Parallel lines with no common view.
No intersection, no point to share,
No solution exists anywhere.
Like trains on separate tracks, they race,
Never to meet in time or space.
So remember these systems, three in all,
Independent, dependent, inconsistent call.
In algebra’s landscape, they play their part,
Solving equations, a mathematical art.
Each type unique, with its own solution,
In the grand mathematical evolution.
Clark Vangilder's Cognitions 