There are several synonyms for the phrase "were dependent on," each with its own slightly different connotation. "Relied on" suggests a degree of trust and necessity, as in "we relied on him to finish the project." "Hinged on" implies that the outcome of a situation is entirely dependent on a particular factor, as in "the success of the event hinged on good weather." "Counted on" is similar to "relied on," but with emphasis on the expectation or obligation involved, as in "we counted on her to be there on time." "Depended upon" is straightforward and widely used, but can sometimes sound formal or archaic, as in "he depended upon his family for financial support".