document.write( "Question 1114412: how to solve x and y if 2^x × 4^y=1 and 4^xy)=1/16? \n" ); document.write( "

Algebra.Com's Answer #729350 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(1) $\"2%5Ex%2A4%5Ey=1\"$ --> $\"2%5Ex%2A2%5E%282y%29=1\"$ --> $\"2%5E%28x%2B2y%29=1\"$ --> $\"x%2B2y=0\"$ --> $\"x+=+-2y\"$

\n" ); document.write( "(2) $\"4%5E%28xy%29=1%2F16\"$ --> $\"xy+=+-2\"$

\n" ); document.write( "Substituting (1) into (2),

\n" ); document.write( " $\"-2y%5E2+=+-2\"$
\n" ); document.write( " $\"y%5E2+=+1\"$
\n" ); document.write( " $\"y+=+1\"$ or $\"y+=+-1\"$

\n" ); document.write( "(a) y=1 --> x = -2
\n" ); document.write( "(b) y = -1 --> x = 2

\n" ); document.write( "Answer: 2 solutions: (x,y) = (-2,1) or (x,y) = (2,-1) \n" ); document.write( "

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