Question

What will the graph of a system of equations look like if two lines have the same slope but different y-intercepts? How many solutions will the system will have?

What are the three ways that systems can be classified and what does that mean for the number of solutions each system will have?

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Answer 1

I have attached a graph of such a system. The two lines have the same slopes but different y-intercepts, this means the lines are parallel, and therefore the system of equations that they represent has no solutions because the lines never intersect.

Going into your next question, there are three ways the system of equations can be classified: the ones that have a solution, with infinitely many solutions, with no solutions.

The graphs of the system of equations that have a solution intersect exactly at one point.

The graphs of the system of equations that have infinitely many solutions are mapped onto each other (are on top of each-other), and therefore have infinite points of intersection.

The graphs of the system of equations that have no solutions never intersect; these are represented by lines that are parallel.

Hope this helps!