2770.21 – Lines! Intersecting!

The number of points common to the graphs of $(x – y + 2)(3x + y – 4) = 0$ and $(x + y – 2)(2x – 5y + 7) = 0$ is:

2
4
6
16
Infinite

Solution

In the figure below, the solid lines are from the equation, $(x – y + 2)(3x + y – 4) = 0$ . The dotted lines are from the equation, $(x + y – 2)(2x – 5y + 7) = 0$ . The solid lines intersect the dotted lines in 4 points (points where solid lines intersect each other or where dotted lines intersect don't count.) The answer is b.