Răspuns :
a+b=1285
a:b=6 rest 4 conform teoremei impartirii cu rest avem a = 6xb+4
atunci revenim la prima ecuatie si inlocuim pe a si obtinem
6xb+4+b=1285
7xb=1285-4
7xb=1281
b=1281:7
b=183
a=1285-b=1285-183=1102
a=1102
a:b=6 rest 4 conform teoremei impartirii cu rest avem a = 6xb+4
atunci revenim la prima ecuatie si inlocuim pe a si obtinem
6xb+4+b=1285
7xb=1285-4
7xb=1281
b=1281:7
b=183
a=1285-b=1285-183=1102
a=1102
x + y = 1 285
x : y = 6 rest 4 ==> x = 6y + 4
x /-----/-----/-----/-----/-----/-----/+4
y /-----/
1 285 - 4 = 1 281
1 281 : 7 = 183 (un segment egal)
x = 6 × 183 + 4 = 1 098+4 = 1 102
y = 183
Verificam:
1 102 + 183 = 1 285
1 102 : 183 = 6 rest 4
x : y = 6 rest 4 ==> x = 6y + 4
x /-----/-----/-----/-----/-----/-----/+4
y /-----/
1 285 - 4 = 1 281
1 281 : 7 = 183 (un segment egal)
x = 6 × 183 + 4 = 1 098+4 = 1 102
y = 183
Verificam:
1 102 + 183 = 1 285
1 102 : 183 = 6 rest 4