Question

Se x e y são números reais tais que $\left \{ {{ 3^{2x+y} =1} \atop { 3^{x-2y} = \frac{1}{9} }} \right.$ , qual o valor de x - y ?

Answer 1

$\left \{ {{3^{2x + y}=1} \atop {3^{x-2y}= \frac{1}{9} }} \right. \\ \\ \left \{ {{3^{2x + y}=3^{0}} \atop {3^{x-2y}= 3^{-2}}} \right. \\ \\ \left \{ {{2x+y = 0} \atop {x-2y=-2}} \right. \\ \\ \left \{ {{4x+2y=0} \atop {x-2y=-2}} \right. \\ \\ 5x = -2 \\ \\ x = -\frac{2}{5} \\ \\ x-2y = -2 \\ \\ - \frac{2}{5} -2y = -2 \\ \\ -2-10y=-10 \\ \\ -10y=-10+2 \\ \\ -10y=-8 \\ \\ y = \frac{8}{10} = \frac{4}{5} \\ \\ x - y = - \frac{2}{5} - \frac{4}{5} = - \frac{6}{5}$

Espero ter ajudado.