Let

Consider the lines and where is the line through parallel to and is the line through parallel to . Prove that these two lines intersect and determine the point of intersection.

*Proof.* We have

Then if and intersect we must have such that

From the second equation we have which implies . Plugging this into the first equation we then have which implies . Therefore, . Then we check these values of satisfy the third equation,

So, the point of intersection is