[latex]1. \left \{ {{x+2y=3} \atop {3^{x-y} =81}} \right. 2. \left \{ {{4^{x} *2 ^{y}=32 } \atop {3^{8x+1} =3^{3y} }} \right. 3. \left \{ {{3^{3x-2y}=81 } \atop {3^{6x} *3^{y} }=27} \right. [/latex]

1) [latex] \left \{ {{x=3-2y} \atop {3^{x-y} =81}} \right.[/latex] [latex] \left \{ {{x=3-2y} \atop {3^{3-2y-y} =81}} \right.[/latex] [latex] \left \{ {{x=3-2y} \atop {3^{3-3y}=3^{4}}} \right.[/latex] [latex]3-3y=4[/latex] [latex]-3y=4-3[/latex] [latex]y=- \frac{1}{3}[/latex] [latex]x=3-2y=3- \frac{2}{3}=\frac{7}{3}=2\frac{1}{3}[/latex] Ответ: [latex](2\frac{1}{3};-\frac{1}{3})[/latex] 2) [latex] \left \{ {{2^{2x+y}=2^{5}} \atop {8x+1=3y}} \right. [/latex] [latex] \left \{ {{2x+y=5} \atop {8x+1=3y}} \right. [/latex] [latex] \left \{ {{y=5-2x} \atop {8x+1=3(5-2x)}} \right. [/latex] [latex]8x+1=15-6x[/latex] [latex]14x=14[/latex] [latex]x=1[/latex] [latex]y=5-2x=5-2=3[/latex] Ответ: (1; 3) 3) [latex]\left \{ {{3^{3x-2y}=3^{4}} \atop {3^{6x+y}=3^{3}} \right. [/latex] [latex]\left \{ {{3x-2y=4} \atop {6x+y=3} \right. [/latex] [latex]\left \{ {{3x-2(3-6x)=4} \atop {y=3-6x} \right. [/latex] [latex]3x-6+12x=4[/latex] [latex]15x=10[/latex] [latex]x= \frac{2}{3} [/latex] [latex]y=3-6x=3-\frac{2*6}{3}=3-4=-1[/latex] Ответ: [latex](\frac{2}{3};-1)[/latex]