Cook the beef, onion, carrots and garlic in a 12-inch skillet over medium-high heat until the beef is well browned, stirring often to separate meat. Pour off any fat.
Stir the tomatoes with juice, soup and water in the skillet and heat to a boil. Reduce the heat to low. Cook for 15 minutes, stirring occasionally. Stir in the basil.
Place the linguine into a large bowl. Add the beef mixture and toss to coat. Serve with the cheese.
Time-Saving: You may substitute 2 cups shredded carrots for the diced carrots in this recipe. Pre-shredded carrots are available in the produce section or salad bar of most grocery stores.