What is the area of the region bounded by the three lines with equations $2x+y = 8$, $2x-5y = 20$ and $x+y = 10$?

  42

Step-by-step explanation:

A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...

  equations 1, 2: A(5, -2)

  equations 2, 3: B(10, 0)

  equations (3, 1): C(-2, 12)

Then the area can be found from the coordinates using the formula ...

  A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|

  = (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|

  A = 42

The area of the triangular region is 42 square units.