Question

Given that a and b are whole numbers, solve for a and b in each of the following.

(a) 2a+3b=18

(b)4a+6b=68

(c)4a+7b=73

(d)3a+8b=47

Answer 1

\(a,2a+3b=18\)

Dễ thấy:\(\hept{\begin{cases}3b⋮3\\18⋮3\end{cases}\Rightarrow18-3b⋮3}\)

\(\Leftrightarrow2a⋮3\left(a\le9\right)\)

Vì \(\left(2;3\right)=1\Rightarrow a⋮3\)

Mà \(a\le9\Rightarrow a=0;3;6;9\)

+) \(a=0\Rightarrow2a=0\Rightarrow3b=18\Rightarrow b=6\)

+)\(a=3\Rightarrow2a=6\Rightarrow3a=12\Rightarrow a=4\)

Bn xét nốt 2 TH nx nhé