Question 651696

 solve 3 to the power x *3 to the power-y= 9 and 2 power y *4 power -x=1/8  

please help me


{{{3^x * (3^(- y)) = 9}}}

{{{3^(x + (- y)) = 9}}}

{{{3^(x - y) = 9}}}

{{{3^(x - y) = 3^2}}}


Since bases are equal, then x – y = 2 ---- eq (i)


{{{2^y * (4^(- x)) = 1/8}}}

{{{2^y * (2^2)^(- x) = 1/8}}}

{{{2^y * (2^(2 * (- x))) = 1/8}}}

{{{2^y * (2^(- 2x)) = 1/8}}}

{{{2^(y + (- 2x)) = 1/8}}}

{{{2^(y - 2x) = 1/8}}}

{{{2^(y - 2x) = 2^-3}}}


Since bases are equal, then: y - 2x = - 3 ---- - 2x + y = - 3 ----- eq (ii)


x – y = 2 ---- eq (i) 
- 2x + y = - 3 ----- eq (ii) 
- x = - 1 ----- Adding eqs (ii) & (i)


{{{highlight_green(x = 1 )}}}


1 – y = 2 -------- Substituting  1 for x in eq (i) 
- y = 2 - 1 
- y = 1


{{{highlight_green(y = - 1)}}}


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