5x+2y=175的所有非负整数解

x y
1 85
3 80
5 75
7 70
9 65
11 60
13 55
15 50
17 45
19 40
21 35
23 30
25 25
27 20
29 15
31 10
33 5
35 0

5x+2y=175,x=35-2y/5=35-2k,其中y=5k,
由x=35-2k≥0得,k≤35/2,由y=5k≥0,得k≥0,
即0≤k≤35/2,故非负整数解为(共18组)
x=35-2k,y=5k,k=0,1,2,...,17
x=35,y=0,
x=33,y=5,
x=31,y=10,
...
x=1,y=85,

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