20x+35y=365、则正整数的解有4x-9y=7?4x+5y=98?

Question

20x+35y=365、则正整数的解有 4x-9y=7?4x+5y=98?

Answer 1

{ 4x - 9y = 7 ①；{ 4x + 5y = 98 ②；把② - ①,可得14y = 91 ；y = 91/14 ；y = 13/2,代入②可得4x + 65/2 = 98 ；4x = 131/2 ；x = 131/8 .综上所述,原方程组的解为：{ x = 131/8 ；{ y = 13/2 .20x + 35y = 365,化简得4x + 7y = 73,所以x = (73 - 7y)/4 ≥ 1,所以73 - 7y ≥ 4,所以69 ≥ 7y,解得y ≤ 69/7 = 9又6/7,所以y = 1,2,3,4,5,6,7,8,9,分类讨论：1）如果y = 1,代入可得x = 66/4不是正整数,舍去；2）如果y = 2,代入可得x = 59/4不是正整数,舍去；3）如果y = 3,代入可得x = 52/4 = 13,符合题意；4）如果y = 4,代入可得x = 45/4不是正整数,舍去；5）如果y = 5,代入可得x = 38/4不是正整数,舍去；6）如果y = 6,代入可得x = 31/4不是正整数,舍去；7）如果y = 7,代入可得x = 24/4 = 6,符合题意；8）如果y = 8,代入可得x = 17/4不是正整数,舍去；9）如果y = 9,代入可得x = 10/4不是正整数,舍去；综上所述,原方程的正整数解为：{ x = 3 ；或者{ x = 6 ；{ y = 13 ； { y = 7 .