This week in math I learned how to tell how many solutions a system can have. A system is a set of equations that you use to find the solution, and there can be either one solution, 0 solutions or infinite solutions.

When there are lines on a graph that don’t intersect there would be 0 solutions. If we use y=mx+b the slope would be the same for both equations but the y intercept would be different which means that the lines are parallel, so they wouldn’t touch anywhere.

When there are lines on the graph that intersect there would be one solution. The slopes would be different therefore the two lines would have to touch.

When there are lines that are equivalent there would be infinite solutions. The two lines have the same slope and the same y intercept therefore they are on top of each other (coincidental lines) and they would be touching forever.

Examples: