2770.21 – Lines! Intersecting!

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

  1. 2

  2. 4

  3. 6

  4. 16

  5. Infinite

Solution

In the figure below, the solid lines are from the equation, (x–y+2)(3x+y–4)=0(x – y + 2)(3x + y – 4) = 0. The dotted lines are from the equation, (x+y–2)(2x–5y+7)=0(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.