x + y = a (1)
5x + 3y = 31 (2)
联立两式,
(2) - (1) * 3 :2x = 31 - 3a
x = (31 - 3a) / 2
得 y = (5a - 31)/2
要令方程组的解为正数,
即x > 0,y > 0
得(31 - 3a) / 2 > 0,(5a - 31) / 2 > 0
化简为 a < 31/3 且 a > 31/5
∴ 31/5 < a < 31/3
且a为整数,∴a = 7,8,9.