Final answer:
The city located on the River Irwell with the River Mersey to the south is Manchester, a key city in the Industrial Revolution in Britain.
Step-by-step explanation:
The city that is located on the River Irwell, with the River Mersey to the south, is Manchester. Manchester was an epicenter during the Industrial Revolution in Britain and witnessed the country's transformation from an industrial powerhouse in northern England to a more diverse, post-industrial economy in the south.
Manchester's historical significance is highlighted by attractions such as the Science and Industry Museum, which details the city's pivotal role in industrial history. Once surrounded by factories and the busy life of workers, it is now a vibrant city with connections to major ports like Liverpool, which has modernized to keep up with changing economic demands.