Resposta:

S={-2, 3}

Explicação passo-a-passo:

[tex]6 {}^{x} .6 {}^{y} = 6[/tex]

[tex]2 {}^{2x} \div 2 {}^{y} = 2 {}^{5} [/tex]

[tex]6 {}^{x + y} = 6[/tex]

[tex]2 {}^{2x - y} = 2 {}^{5} [/tex]

[tex]x + y = 1[/tex]

[tex]2x - y = 5[/tex]

[tex] - - - - - - - - - - - - - [/tex]

[tex]3x = 6 \\ x = \frac{6}{2} [/tex]

[tex]x = 3[/tex]

[tex]x + y = 1 \\ 3 + y = 1 \\ y = 1 - 3 \\ y = - 2[/tex]

Verified answer

[tex]\large\bm{\begin{cases} {6}^{x} \times {6}^{y} = 6 \\ {4}^{x} \div {2}^{y} = 32 \end{cases}} \\\\\large\bm{} \begin{cases} {6}^{x + y} = {6}^{1} \\ {2}^{2x } \div {2}^{y} = {2}^{5} \end{cases} \\ \\ \large\bm{}\begin{cases}x + y = 1 \\ {2}^{2x - y} = {2}^{5} \end{cases} \\\\ \large\bm{}\begin{cases}x + y = 1 \\ 2x - y = 5 \end{cases} \\ \\ \large\bm{\left(x,y\right)} = \left(2, - 1\right) \\ \\ \large\bm{}\begin{cases} {6}^{2} \times {6}^{ - 1} = 6 \\ {4}^{2} \div {2}^{ - 1} = 32 \end{cases} \\ \\ \large\bm{}\begin{cases}6 = 6 \\ 32 = 32\end{cases} \\ \\ \large\bm{S \{ \left(x,y\right) =\left(2, - 1\right) } \}[/tex]

[tex]{\large\boxed{\boxed{  { \large \bm{ Bons~Estudos} }}}}[/tex]