Notice that 2042 is even. The only way for two primes to add to an even number is if one of them is 2 (because all other primes are odd, and the sum of two odd numbers is even).
Assume one prime is 2. Then:
q = 2042 - 2 = 2040
Check if 2040 is prime. It is divisible by 2, 3, 5, etc., so 2040 is not prime.
Conclusion: There are no two prime numbers that add to 2042.
Answer: No solution exists; 2042 cannot be expressed as the sum of two primes.