Here's why it's difficult to give a precise number:
* We haven't found all the stars: We've only cataloged a small fraction of the stars in the Milky Way.
* Exoplanet detection is ongoing: We are constantly discovering new exoplanets (planets outside our solar system), and our methods are improving.
* We don't know the frequency of planetary systems: While we've found many planets, we don't know how common it is for stars to have planets, or how many planets are typically in a system.
However, some estimates suggest that there could be hundreds of billions, or even trillions of solar systems in our galaxy. This is based on:
* The number of stars in the Milky Way (estimated at hundreds of billions)
* The increasing discovery rate of exoplanets
* Statistical models that try to extrapolate from known data
So, while we don't have a definitive answer, the number of solar systems in the Milky Way is likely vast.
