A nutritionist, working for NASA, must meet certain minimum nutritional requirements and yet keep the weight of the food at a minimum. He is considering a combination of two foods, which are packaged in tubes. Each tube of food A contains 4 units of protein, 2 units of carbohydrates, and 2 units of fat and weighs 2 pounds. Each tube of food $B$ contains 3 units of protein, 6 units of carbohydrates, and 1 unit of fat and weighs 2 pounds. The requirement calls for 48 units of protein, 42 units of carbohydrates, and 18 units of fat. How many tubes of each food should be supplied to the astronauts?

The number of tubes of food $A$ is $\square$.
(Simplify your answer.)
The number of tubes of food $B$ is $\square$.
(Simplify youlfr answer.)

Step 1 ：Let's denote the number of tubes of food A as x and the number of tubes of food B as y. We can then set up the following equations based on the information given in the problem:

Step 2 ：\(4x + 3y = 48\) (This equation represents the protein requirement)

Step 3 ：\(2x + 6y = 42\) (This equation represents the carbohydrates requirement)

Step 4 ：\(2x + y = 18\) (This equation represents the fat requirement)

Step 5 ：The system of equations is overdetermined, meaning there are more equations than unknowns. This can sometimes lead to no solution. However, in this case, we can observe that the second equation (carbohydrates) is a multiple of the third equation (fat). This means we can eliminate one of these equations without losing any information.

Step 6 ：Let's eliminate the second equation and solve the system again with the remaining two equations:

Step 7 ：\(4x + 3y = 48\)

Step 8 ：\(2x + y = 18\)

Step 9 ：Solving this system of equations gives us the solution: \(x = 12, y = 3\)

Step 10 ：Final Answer: The number of tubes of food A is \(\boxed{12}\) and the number of tubes of food B is \(\boxed{3}\)