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Rudolff's Problem


Negatively Triangular

Age 14 to 16 Challenge Level:

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?