Negatively triangular

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

Problem

Negatively Triangular printable sheet

 

Four straight lines have the following equations:

$$\begin{align} 3x+8y&=59 \\ x-2y&=1 \\ y-4x&=3 \\ 3y+2x &= -19 \end{align}$$

 

How many points of intersections do you expect there to be?

Three of the four lines enclose a triangle which only has negative co-ordinates for all points on that triangle.

Which three lines?