Final answer:
The state with Eugene and Corvallis is Oregon. The joint occupation of the Oregon Territory was between Britain and the United States according to treaties signed in 1818 and 1827.
Step-by-step explanation:
The state that has both Eugene and Corvallis is Oregon. In historical context regarding the expansion of the United States, Oregon was a significant territory. During the 19th century, there were competing claims for the Oregon Territory by Spain, Russia, Britain, and the United States. Ultimately, Spain and Russia withdrew their claims. The joint occupation of the Oregon Territory was between Britain and the United States based on the treaties signed in the years 1818 and 1827. This joint occupation continued until the mid-1840s when the United States strengthened its claim as a result of increased American settlement, thanks in part to the westward migration inspired by "Oregon Fever".