RĂ©soudre dans \(\mathbb{R}^2\) les systĂšmes suivants :

\[ \begin{array}{ll} (S_1) : \begin{cases} 3^x + 7^y = 16 \\ 3^x - 7^y = 2 \end{cases} & (S_2) : \begin{cases} 2^{x-2} \cdot 2^{y-1} = 1 \\ 2^x + 2^y = 5\sqrt{2} \end{cases} \\ \\ (S_3) : \begin{cases} 4^x \times 5^y = 5^{2x+1} \\ 20^x + 25^y = 5^{2y+1} \end{cases} & (S_4) : \begin{cases} 2^{x+y} = 16\sqrt{2} \\ 2^x + 2^{x-y} = 12\sqrt{2} \end{cases} \\ \\ (S_5) : \begin{cases} e^{\frac{x}{x-1}} + e^{\frac{y}{y+1}} = 13 \\ e^{\frac{2xy+x-y}{(x-1)(y+1)}} = 42 \end{cases} & (S_6) : \begin{cases} 5^x \cdot 5^{2y} = 25 \\ \log_3 x + \log_3 (2y+3) = 1 \end{cases} \end{array} \]