1. A monitoring system comprising: a plurality of image-capturing apparatuses including an event detector configured to process first event detection on a corresponding captured image for a first event, and a transmission configured to output to a network a processing result of the first event detection without the image when a request for the image is not received and to output to the network a processing result of the first event detection with the captured image when the request for the image is received; and a management apparatus including a receiving unit that receives data from the plurality of image-capturing apparatuses via the network, an event determination unit that determines occurrence of a second event in accordance with the received processing result of the first event detection, and a request sending unit that sends the request for the image to the image-capturing apparatus when the second event occurs, wherein the second event is at least one of moving object detection and non-moving object detection.