SOLUTION: how do I find out with a graph that already has the points plotted if it has no solutions, one, or many?

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Question 1063259: how do I find out with a graph that already has the points plotted if it has no solutions, one, or many?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Let's say you have four points A,B,C,D plotted on the same xy grid. Let's further say that you know A and B lie on the same line. So that means we can draw a line through A and B. Call this line m.

If C and D are on the other line, then draw a line through those two points. Call this line n.

There are 3 different possible scenarios

Scenario 1: Line m and line n cross at exactly 1 point. This is the point of intersection and it is the solution to the system. This system has 1 solution.

Scenario 2: The two lines are parallel. This can be visually confirmed or you can determine the slope of each line. The two lines would have equal slopes but different y intercepts if they are parallel. There are no solutions (since the lines never cross)

Scenario 3: The two lines are actually one in the same. One line is perfectly right on top of the other line. This means there are infinitely many solutions.