Question

How can I tell if a system of equations has one, no, or infinitely many solutions?

Answer 1

There are many ways to interpret if whether or not a system of equations has solutions or not. Here is one way that is most ideal for most, if not, all equations: using graphs.

• If the graphs of the set of equations do NOT intersect, then there are no solutions (because no x or y value will ever make both equations true)
• If the graphs of the set of equations DO intersect at one point, then ONLY that one point will make both equations true. (One solution)
• If the graphs of the set of equations are identical on the graph, then there are infinite solutions that make both equations true.