The equations of the three lines must be considered in pairs to
find the coordinates of their points of intersection, i.e. the
coordinates of the vertices of the triangle. By solving each pair
of simultaneous equations, you should find that the coordinates are
$(-15,-9)$, $(0,6)$ and $(5,1)$. The area of the triangle may now
be found by enclosing the triangle in a rectangle and subtracting
the areas of the three surrounding triangles from the area of the
rectangle. This gives $300 - (112½ + 12½ +
100) = 75$.
This problem is taken from the UKMT Mathematical Challenges.