Question

If the graphs of two lines in a system do not intersect at any point, what can you conclude about the solution of the system. Why? Explain?

Would that make it a no solution ?

Answer 1

If no solution is present, the lines are either parallel or collinear. If they're collinear there are infinite solutions.

Answer 2

Lines are made up of points that satisfy an equation. Where the lines intersect is a solution. For a 2 line system, there are two main cases: either they the lines intersect, or they don't. When they do not intersect, none of the points in one line are in the other line, and vice versa. Since they don't intersect, there isn't a solution. Algebraically that's like saying when you find an (x,y) that makes one equation work, it's guaranteed to make the other equation not work.

Answer 3

When two lines actually do intersect, they can either intersect at exactly one of their points, or they can intersect for all of their points. There is no in-between. For the case where they intersect for all of their points, the only way this could happen is if the two lines are actually the same line. This means you can convert one equation to the other equation using algebra .

Answer 4

For the case where there is only one solution, the lines don't have the same slope. This isn't as relevant to your question though.