SOLUTION: {{{9x^2+25y^2=46}}}, {{{xy=-1}}}. Find {{{3x+5y}}}

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Question 123341: 9x%5E2%2B25y%5E2=46, xy=-1. Find 3x%2B5y
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E2%2B25y%5E2=46, xy=-1. Find 3x%2B5y

Notice that 

%283x%2B5y%29%5E2=9x%5E2%2B30xy%2B25y%5E2, so

%283x%2B5y%29%5E2=%289x%5E2%2B25y%5E2%29%2B30xy, and since 9x%5E2%2B25y%5E2=46,

%283x%2B5y%29%5E2=46%2B30xy, and since xy=-1,

%283x%2B5y%29%5E2=46%2B30%28-1%29, or

%283x%2B5y%29%5E2=46-30, or

%283x%2B5y%29%5E2=16. Taking square roots of both sides:

3x%2B5y= ±4.

Edwin