Why were merchants and artisans unable to vote for changes in their city-states

Because they didn't own land so they weren't considered citizens, is the right answer.

Explanation:

The merchants and the artists in the ancient world were involved in the activities that had a lot to do with trade. The people of this section were involved in the production and marketing of various products. Since they had to move from one place to another for their work they did not hold any property. Due to the lack of holdings, they were not given voting rights. Thus they could not participate in the political activities.