3N + 4M = 230; 5N = 8M = 390

Question

Please solve this.

Answer 1

If 5N=390 then N=78; and if 8M=390 then M=48.75. 3N+4M=234+195=429, so it cannot also equal 230 as given by the first equation. The system is inconsistent and there is no solution.

Comments

If the second half is supposed to read 5N+8M=390, then, doubling the first equation, we have 6N+8M=460, and M can be eliminated: N=460-390=70, by subtraction; and 4M=230-210=20. So M=5. Solution: M=5, N=70.