Question

PERGUNTA SOBRE: SISTEMA EXPONENCIAL $\left \{ {{8^x.4^y=\frac{1}{4} } \atop {4^x.2^-y=2}} \right.$ (FUVEST-SP)

Answer 1

8=2³

4=2²

(2³)^x.(2²)^y=1/2²

(2)^3x.(2)^2y=2^-2

2^(3x+2y)=2^-2

3x+2y=-2

(2²)^x.(2)^-y=2

(2)^(2x-y)=2¹

2x-y=1

3x+2y=-2

2x-y=1

y=1-2x

3x+2(1-2x)=-2

3x+2-4x=-2

x=4

y=-7

$\boxed{ \boxed{ \boxed{ \mathsf{ {x = 4 \: \: e \: \: y = - 7}}}}}$

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