The presence of black holes in a galaxy does not necessarily mean that they will have a significant impact on the motion of our solar system. The reason is primarily due to the vast distances involved and the relative sizes of objects within a galaxy.
Black holes, including supermassive black holes found at the centers of galaxies, have extremely strong gravitational fields. However, their gravitational influence diminishes rapidly with distance. In the case of our solar system, the nearest known black hole, named Sagittarius A*, is located at the center of our Milky Way galaxy, approximately 26,000 light-years away. Despite its enormous mass, its gravitational pull on our solar system is not significant enough to significantly affect the orbits of the planets or other objects within it.
The gravitational interactions within a galaxy are primarily determined by the combined mass of all the stars, gas, and dark matter present. The motions of stars within a galaxy are primarily influenced by the overall gravitational field created by the distribution of mass throughout the galaxy. The presence of black holes can affect the motion of nearby stars, but their influence decreases with distance.
In summary, while black holes have a powerful gravitational pull, the vast distances between objects in galaxies, including our solar system, mitigate their effects on individual star systems like ours. The motions within a galaxy are primarily determined by the collective gravitational interactions of all the objects within it, including the distribution of normal matter and dark matter.