Bài 2:

Ta có:

+) a + b + c + d = 1

a + c + d = 2

\(\Rightarrow\) b = 1 - 2 = -1

+) a + b + c + d = 1

a + d + b = 3

\(\Rightarrow\) c = 1 - 3 = -2

+) a + b + c + d = 1

a + b + c = 4

\(\Rightarrow\) d = 1 - 4 = -3

+) a + b + c + d = 1

\(\Rightarrow\) a + (-1) + (-2) + (-3) = 1

\(\Rightarrow\) a + \(\left[\text{(-1) + (-2) + (-3) }\right]\) = 1

\(\Rightarrow\) a + (-6) = 1

\(\Rightarrow\) a = 1 - (-6)

\(\Rightarrow\) a = 7

Vậy \(\left\{\begin{matrix}a=7\\b=-1\\c=-2\\d=-3\end{matrix}\right.\)

Ta có: \(\overline{abcdeg}\) = 10000.\(\overline{ab}\) + 100.\(\overline{cd}\) + \(\overline{eg}\)

= (9999.\(\overline{ab}\) + 99.\(\overline{cd}\) ) + ( \(\overline{ab}\) + \(\overline{cd}\) + \(\overline{eg}\))

Theo bài ra, ta có: \(\overline{ab}\) + \(\overline{cd}\) + \(\overline{eg}\) \(⋮\) 11

Vì 9999.\(\overline{ab}\) + 99.\(\overline{cd}\) \(⋮\) 11 và \(\overline{ab}\) + \(\overline{cd}\) + \(\overline{eg}\) \(⋮\) 11

nên (9999.\(\overline{ab}\) + 99.\(\overline{cd}\) ) + ( \(\overline{ab}\) + \(\overline{cd}\) + \(\overline{eg}\)) \(⋮\) 11

Vậy \(\overline{abcdeg}\) \(⋮\) 11