B3. Calculate for which values of the parameter $m$ the lines with equations $y=(m+5) x+m-1$ and $y=(m-1)^{2} x-3 m-6$ are parallel.
B3. Parallel lines have the same slope. Therefore, it must hold that $m+5=(m-1)^{2}$. We rearrange the equation to $m^{2}-3 m-4=0$ and factorize it as $(m-4)(m+1)=0$. The solutions are $m=4$ and $m=-1$.

Observation or use that the slopes are equal $k_{1}=k_{2} \ldots \ldots \ldots \ldots \ldots \ldots 1$ point Writing or using the slopes $k_{1}=m+5$ and $k_{2}=(m-1)^{2} \ldots \ldots \ldots \ldots 1+1$ point Writing the rearranged quadratic equation $m^{2}-3 m-4=0 \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-14.jpg?height=58&width=1687&top_left_y=1196&top_left_x=230)

![](https://cdn.mathpix.com/cropped/2024_06_07_d6b556bd14f8001ca6fag-14.jpg?height=49&width=1685&top_left_y=1249&top_left_x=228)