HP50g or other: U. of Houston calc exams

[Peter Murphy]

The following problem, from the 2013 Houston calculator exam, seems conceptually simple to solve, but the manipulations necessary to solve it from start to finish on the 50g are not so obvious:

14. There are 3 points of intersection of pairs of the lines 2x+3y=4, 7x-2y=3 and
x+y=15. Give the area of the triangle determined by these three points.

It seems clear that the "shoelace formula" of Meister and Gauss* is needed, and a little program to apply that would be nice.

Peter

* <https://en.wikipedia.org/wiki/Shoelace_formula>