Is there such an integer a that the solution of the system of equations 3x + 4Y = a4x + 3Y = 5 is a pair of non negative numbers? If it exists, find its solution; if it does not exist, give the reason

Is there such an integer a that the solution of the system of equations 3x + 4Y = a4x + 3Y = 5 is a pair of non negative numbers? If it exists, find its solution; if it does not exist, give the reason

From the original equations, 9x + 12Y = 3A (1) 16x + 12Y = 20 (2) (2) - (1), x = 20 − 3a7, substituting (1), y = 4A − 157; ∵ XY is a pair of non negative numbers, ∵ 20 − 3a7 ≥ 04A − 157 ≥ 0, that is, 20 − 3a ≥ 04A − 15 ≥ 0, solution 334 ≤ a ≤ 623; ∵ A is an integer, ∵ A is 4,5,6, there is such an integer a