document.write( "Question 842617: Solve for X and Y :\r
\n" ); document.write( "\n" ); document.write( "8/x + 6/y = 6 and 1/x + 1/y = 1/6 \n" ); document.write( "

Algebra.Com's Answer #507659 by LinnW(1048) $\"\"$ $\"About$

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8/x + 6/y = 6 and 1/x + 1/y = 1/6
\n" ); document.write( "8/x + 6/y = 6 and 1/x + 1/y = 1/6
\n" ); document.write( "multiply the second equation by 36
\n" ); document.write( "36( 1/x + 1/y = 1/6 ) = 36/x + 36/y = 6
\n" ); document.write( "Since 8/x + 6/y = 6
\n" ); document.write( "8/x + 6/y = 36/x + 36/y
\n" ); document.write( "add -8/x -6/y to each side
\n" ); document.write( "0 = 28/x + 30/y
\n" ); document.write( "add -30/y to each side
\n" ); document.write( " $\"-30%2Fy+=+28%2Fx\"$
\n" ); document.write( "do cross products
\n" ); document.write( "28y = -30x
\n" ); document.write( "divide by 28
\n" ); document.write( "y = $\"%28-30%2F28%29%2Ax\"$
\n" ); document.write( "substitute $\"%28-30%2F28%29%2Ax\"$ for y in 1/x + 1/y = 1/6
\n" ); document.write( " $\"1%2Fx+%2B+1%2F%28%28-30%2F28%29%2Ax%29+=+1%2F6\"$
\n" ); document.write( " $\"1%2Fx+-+1%2F%28%2830%2F28%29%2Ax%29+=+1%2F6\"$
\n" ); document.write( " $\"1%2Fx+-+28%2F%2830%2Ax%29+=+1%2F6\"$
\n" ); document.write( " $\"%2830%2F30%29%2A%281%2Fx%29+-+28%2F%2830%2Ax%29+=+1%2F6\"$
\n" ); document.write( " $\"%2830%2F%2830%2Ax%29%29+-+28%2F%2830%2Ax%29+=+1%2F6\"$
\n" ); document.write( " $\"%282%2F%2830%2Ax%29%29++=+1%2F6\"$
\n" ); document.write( "do cross products
\n" ); document.write( "30x=12
\n" ); document.write( "divide each side by 30
\n" ); document.write( "x = 12/30 = 2/5
\n" ); document.write( "We previously determined that y = $\"%28-30%2F28%29%2Ax\"$ ,
\n" ); document.write( "so substituting 2/5 for x we have
\n" ); document.write( "y = $\"%28-30%2F28%29%2A%282%2F5%29\"$
\n" ); document.write( "y = $\"%28-60%2F140%29\"$ = $\"-3%2F7\"$
\n" ); document.write( "summarizing x = 2/5 , y = -3/7 \n" ); document.write( "

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