I'm in 1st year university so please keep answering on that level, thanks

Question 1 (10 points) Linear equations Solve the linear equation x + 5y = 16 under each of the following constraints: a) x and y are real numbers (4 points) b) x and y are positive integers (3 points) c) x and y are prime numbers (3 points) A prime number is a positive integer which is solely divisible by 1 and itself. Write conveniently the set of solution(s) in each case. Hint: Write the augmented matrix under REF form and discuss the existence and the number of solutions Question 2 (10 points) Using Gauss-Jordan method, solve the following systems of linear equations whose augmented matrices are given by: 0 1 0 0 0 -1 0 2 a) 0 0 0 0 1 -1 b) 0 2 -1 0 0 0 0 0 0 0 - 0 0 0 0 (6 points) (4 points) Question 3 (15 points) Purchasing aircrafts The Air Force expects to modernize its combat arsenal. It plans to acquire 12 fighter planes of three different types (identified A, B and C) depending on the range of action. The Federal government has allocated a budget of 900 million dollars for this purpose. What should be the number of acquired aircraft of each type knowing that an A-type fighter costs $30 million, a B-type is $50 million and a C-type is $90 million? Use the Gauss-Jordan method as a solution method