Question 1110388
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<pre>
The system


25^x = 125 * 5^y    (1)
(4^x) * (8^-y)=1    (2)


is equivalent to


{{{5^(2x)}}} = {{{5^(3+y)}}}    (1')
{{{2^(2x-3y)}}} = {{{2^0}}}     (2')


Which in turn is equivalent to

2x = 3 + y           (1'')
2x - 3y = 0.         (2'')


============>

2x -  y = 3
2x - 3y = 0
------------------------Subtract to get

     -y - (-3y) = 3  ====>  -y + 3y = 3  ====>  2y = 3  ====>  y = {{{3/2}}}


====>  2x = {{{3*(3/2)}}} = {{{9/2}}}  ====>  x = {{{9/4}}}.


<U>Answer</U>.  x = {{{9/4}}},  y = {{{3/2}}}.
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