When a is an integer, the solutions of the equations x + Y-A = 0.5x + 3Y = 31 about X and y are integers?

When a is an integer, the solutions of the equations x + Y-A = 0.5x + 3Y = 31 about X and y are integers?

X+Y-A=0（1）
5X+3Y=31（2）
(2) (1) × 3
2x+3A=31；
2x=31-3A;
x=（31-3A）/2;
Bring in (1)
(31-3A)/2+Y-A=0;
Y=A-(31-3A)/2=(5A-31)/2;
The solution is an integer
So 5A and 3a need to be odd;
So a must be an odd integer to satisfy the condition
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When a takes what integer solution, the solution of the equations {x + y = a, 5x + 3Y = 31 is positive?

It is necessary to solve this system of equations
x=(31-3a)/2
So: 31-3a > 0
a0
a>31/5
So 31 / 5

When a takes what value, the solution of the equations x + y = a, 5x + 3Y = 31 is a positive integer

Sorry, the calculation was wrong just now. If x = 31 / 2-3a / 2, then A0, then a > 31 / 5, so a = 7 or 9