a)
[tex]\it \begin{cases} \ \it \dfrac{x}{2}=\dfrac{y}{3} \Rightarrow x=\dfrac{2y}{3}\\ \\ \\ \it x+8y=52 \Rightarrow x=52-8y\end{cases} \Rightarrow \dfrac{2y}{3}=52-8y\Big|_{\cdot3} \Rightarrow 2y=3\cdot52-24y \Rightarrow\\ \\ \\ \Rightarrow 2y+24y=3\cdot52 \Rightarrow 26y=3\cdot52|_{:26}\Rightarrowy=3\cdot2 \Rightarrow y=6\\ \\ \\ x=\dfrac{2\cdot6}{3} \Rightarrow x=4\\ \\ S=\{(4,\ 6)\}[/tex]
b)
[tex]\it \begin{cases}\ \it\dfrac{x}{5}=\dfrac{y}{4} \Rightarrow y=\dfrac{4x}{5}=0,8x\\ \\ \\ \it 2x-y=-6 \Rightarrow y=2x+6\end{cases} \Rightarrow 2x+6=0,8x|_{\cdot10}\ \Rightarrow 20x+60=8x\ \Rightarrow \\ \\ \\ \Rightarrow 20x-8x=-60 \Rightarrow 12x=-60|_{:12} \Rightarrow x=-5\\ \\ \\ y=0,8\cdot(-5) \Rightarrow y=-4\\ \\ \\ S=\{(-5,\ -4)\}[/tex]
