Răspuns:
(a,b) = { (1,10);(4,8);(7,6);(10,4);(13,2),(16,0) }
Explicație pas cu pas:
[tex]2a+3b = 32 \\ \\ 3b = 32 - 2a \\ \\ 3b = 2(16-a) \\ \\ \\\boxed{b = \dfrac{2(16-a)}{3}}\quad (*)\\ \\ \Rightarrow 16- a \,\,\vdots\,\,3\Rightarrow 16-a \in \{0,3,6,9,12,15,18,.....\} \Big|-16 \Rightarrow \\ \\ \Rightarrow -a\in \{-16,-13,-10,-7,-4,-1,2,...\} \Rightarrow \\ \\ \Rightarrow a\in \{1,4,7,10,13,16\}\\ \\\text{Inlocuim fiecare valoarea a lui a in relatia }(*)\\ \\ \Rightarrow b\in \{10,8,6,4,2,0\}\\ \\\\\\\Rightarrow (a,b) = \Big\{(1,10);(4,8);(7,6);(10,4);(13,2),(16,0)\Big\}[/tex]
