SOLUTION: 2^x - 3^y = 5 2^(x+2) + 3^(y+2) = 59. find xy

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Question 1209565: 2^x - 3^y = 5
2^(x+2) + 3^(y+2) = 59.
find xy
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

system%282%5Ex+-+3%5Ey+=+5%2C%0D%0A2%5E%28x%2B2%29+%2B+3%5E%28y%2B2%29+=+59%29

system%282%5Ex+-+3%5Ey+=+5%2C%0D%0A2%5E2%2A2%5Ex+%2B+3%5E2%2A3%5Ey+=+59%29

system%282%5Ex+-+3%5Ey+=+5%2C%0D%0A4%2A2%5Ex+%2B+9%2A3%5Ey+=+59%29

Multiply the 1st equation by -4

system%28-4%2A2%5Ex+%2B4%2A3%5Ey+=+-20%2C%0D%0A4%2A2%5Ex+%2B+9%2A3%5Ey+=+59%29

Adding them gives

13%2A3%5Ey=39

3%5Ey=39%2F13

3%5Ey=3

y=1

Go back to 

system%282%5Ex+-+3%5Ey+=+5%2C%0D%0A4%2A2%5Ex+%2B+9%2A3%5Ey+=+59%29

Multiply the 1st equation by 9

system%289%2A2%5Ex+-+9%2A3%5Ey+=+45%2C%0D%0A4%2A2%5Ex+%2B+9%2A3%5Ey+=+59%29

Adding them gives

13%2A2%5Ex=104
2%5Ex=104%2F13
2%5Ex=8
x=3

So xy = (3)(1)=3

Edwin