1. A projection system including multiple projection apparatuses, the projection system comprising: a first projection unit configured to project a first pattern image on a first projection area; a second projection unit configured to project a second pattern image on a second projection area, the second projection area partially overlapping the first projection area; and a first image capturing unit configured to, when the first pattern image is projected on the first projection area, perform first image capture to obtain a first captured image by capturing an image capture area including the first projection area and at least a portion of a second projection area and, when the second pattern image is projected on the second projection area, perform second image capture to obtain a second captured image by capturing the image capture area, wherein the first projection unit is configured to project a first partial projection-target image extracted from a projection target image based on the first captured image, the second captured image, and the projection target image on the first projection area, and wherein the second projection unit is configured to project a second partial projection-target image extracted from the projection target image based on the first captured image, the second captured image, and the projection target image on the second projection area, an image-length-information determining unit configured to determine image length information including lateral length of the first pattern image, length of the second pattern image, and lateral length of an overlapping portion between the first pattern image and the second pattern image using the first captured image and the second captured image; a first generation unit configured to generate first extraction information, the first extraction information specifying an extraction position at which the first partial projection-target image is to be extracted from the projection target image, based on the image length information and lateral length of the projection target image; a first extraction unit configured to extract the first partial projection-target image from the projection target image using the first extraction information; a second generation unit configured to generate second extraction information, the second extraction information specifying an extraction position at which the second partial projection-target image is to be extracted from the projection target image, based on the image length information and the lateral length of the projection target image; and a second extraction unit configured to extract the second partial projection-target image from the projection target image using the second extraction information.