A three-dimensional object printer ejects drops of a build material from a plurality of ejectors in a first printhead to form an object on a first region of a member and ejects drops of a support material from a plurality of ejectors in a second printhead to support the object on the first region of the member. The second printhead ejects drops of the support material onto a second region of the member that is separate from the first region to form a substrate layer. The first printhead ejects drops of the build material onto the substrate layer to form a printed test pattern. An image sensor generates image data of the printed test pattern to identify an inoperable ejector in the first printhead.