# Three Possibilities

When you've got two linear equations, there are three possible scenarios that can occur when you're asked to find their intersection.

Description | Identifying | Example |
---|---|---|

The lines intersect at exactly one point. | Your solution ends up with two values. |
If you apply the substitution method from the previous section, you'll get (1, 4) as the solution. |

The lines don't intersect, i.e. they're parallel. | At some point during your calculations, you reach an obviously false statement, e.g. 3 = -2. |
If you apply the substitution method from the previous section, you'll get 4 = -1. That's not true for any value of |

The lines intersect at every point, i.e. they overlap. | At some point during your calculations, you reach a statement that's always true, e.g. -2 = -2. |
If you apply the substitution method from the previous section, you'll get 4 = 4. That's true for every value of |