1. All mi are distinct and the three systems of equations {y = mix+bi, y =

![0_image_0.png](0_image_0.png)

mjx+bj} (i 6= j ∈ {1, 2, 3}) yield three different solutions. Geometrically, this means that all three lines intersect with three different intersection points. The transformation property follows from the fact that the three intersection points determine the configuration.

2. All mi are distinct and at least two of the three systems of equations {y =

![0_image_1.png](0_image_1.png)

mix+bi, y = mjx+bj} (i 6= j ∈ {1, 2, 3}) have a common solution. Then, obviously, the single solution is common to all three equation systems.

Geometrically, this means that all three lines intersect at the same point.

Take this point and a second point on one of the lines. By drawing parallels through this second point, we obtain two more points, one on each of the other two lines, such that the four points form a parallelogram.

The transformation property now follows from the fact that any two nondegenerate parallelograms can be transformed into each other by an affine bijection.

![0_image_2.png](0_image_2.png)

![0_image_3.png](0_image_3.png)

