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Solve the system x/(sqrt(x) + sqrt(y)) = 18 and y/(sqrt(x) + sqrt(y)) = 2.

 Dec 17, 2019
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x/(sqrt(x) + sqrt(y)) = 18 and y/(sqrt(x) + sqrt(y)) = 2.

x = 18 *(sqrt x sqrt y)        y = 2(sqrtx+ sqrty)                        Multiply 2nd equation by -9  then add both equations...

                                       -9y = -18 (sqrtx+ sqrty)

 

x-9y = 0       x = 9y

 

y = 2 (sqrt(9y) + sqrty)

         y=2 sqrty (sqrt 9+1) 

          y = 8 sqrty

          y^2 = 64 y

          y= 64

                       x = 9y = 576              

 Dec 17, 2019

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